I searched about but didn't find my answer and even asked some clergymen but no result! I know in the other religions women wore hijab like Jews but as we know in Arabian peninsula most people were idolators and had no religion (one god). Was there any hijab for women before Islam?
Acctually No, although there is, it was not called hijab. as described hadith below at the time of the prophet Muhammad (PBUH).
(the wife of the Prophet) 'Umar bin Al-Khattab used to say to Allah's Apostle "Let your wives be veiled" But he did not do so. The wives of the Prophet used to go out to answer the call of nature at night only at Al-Manasi.' Once Sauda, the daughter of Zam'a went out and she was a tall woman. 'Umar bin Al-Khattab saw her while he was in a gathering, and said, "I have recognized you, O Sauda!" He ('Umar) said so as he was anxious for some Divine orders regarding the veil (the veiling of women.) So Allah revealed the Verse of veiling. (Al-Hijab; a complete body cover excluding the eyes). (See Hadith No. 148, Vol. 1)
and described also in Surah An-Nūr (The Light) ayah 31.
وَقُل لِّلْمُؤْمِنَاتِ يَغْضُضْنَ مِنْ أَبْصَارِهِنَّ وَيَحْفَظْنَ فُرُوجَهُنَّ وَلَا يُبْدِينَ زِينَتَهُنَّ إِلَّا مَا ظَهَرَ مِنْهَا ۖ وَلْيَضْرِبْنَ بِخُمُرِهِنَّ عَلَىٰ جُيُوبِهِنَّ ۖ وَلَا يُبْدِينَ زِينَتَهُنَّ إِلَّا لِبُعُولَتِهِنَّ أَوْ آبَائِهِنَّ أَوْ آبَاءِ بُعُولَتِهِنَّ أَوْ أَبْنَائِهِنَّ أَوْ أَبْنَاءِ بُعُولَتِهِنَّ أَوْ إِخْوَانِهِنَّ أَوْ بَنِي إِخْوَانِهِنَّ أَوْ بَنِي أَخَوَاتِهِنَّ أَوْ نِسَائِهِنَّ أَوْ مَا مَلَكَتْ أَيْمَانُهُنَّ أَوِ التَّابِعِينَ غَيْرِ أُولِي الْإِرْبَةِ مِنَ الرِّجَالِ أَوِ الطِّفْلِ الَّذِينَ لَمْ يَظْهَرُوا عَلَىٰ عَوْرَاتِ النِّسَاءِ ۖ وَلَا يَضْرِبْنَ بِأَرْجُلِهِنَّ لِيُعْلَمَ مَا يُخْفِينَ مِن زِينَتِهِنَّ ۚ وَتُوبُوا إِلَى اللَّهِ جَمِيعًا أَيُّهَ الْمُؤْمِنُونَ لَعَلَّكُمْ تُفْلِحُونَ
And tell the believing women to reduce [some] of their vision and guard their private parts and not expose their adornment except that which [necessarily] appears thereof and to wrap [a portion of] their headcovers over their chests and not expose their adornment except to their husbands, their fathers, their husbands' fathers, their sons, their husbands' sons, their brothers, their brothers' sons, their sisters' sons, their women, that which their right hands possess, or those male attendants having no physical desire, or children who are not yet aware of the private aspects of women. And let them not stamp their feet to make known what they conceal of their adornment. And turn to Allah in repentance, all of you, O believers, that you might succeed.
Beside the fact that Jews and Christians used to live in the Arabian peninsula before Islam and the fact that the Torah already included verses about veiling the hair. The jahili poetry is full of statements speaking about veils, as khimar, naseef or hijab among them the poem of the "mujaradah" which we may translate "the naked lady" of an-Nabighah a-Dhubyani where he says:
سقَطَ النّصيفُ ولم تُرد إسقاطه * فتناولته واتّقتنا باليدِ
(My own translation)
The veil felt and she didn't want to let it down *
then she toke it and hid herself from us (our views) by her hands
This shows the importance of hiding faces for ladies especially by tribes in Urban regions it was very important for a woman not to show off her face for foreigners and out side of the house.
Sakhr the brother of the famous (female) poet al-Khansa' said about her:
(My own translation)
By Allah I will not give her (in marriage) to the worst (of people) * as if I died (or perished) she would burst her khimar * and she would wear her hair instead of a waistcoat
This shows that a good lady would never show her hair nor her face off unless she was in grief!
This is also the topic of this jahili poem of ar-Rabi' ibn Ziyah al-'Absi الربيع بن زياد العبسي after the killing of Malik ibn Zuhair مالك بن زهير:
من كان مسرورًا بمقتل مالك * * * فليـأت نسوتنا بوجه نهـار
Whom (ever) was happy (joyful) about the death (killing) of Malik * * * Let him come and see our women at the day time
يجد النسـاء حواسرًا يندبنه * * * يلطمن أوجههن بالأسحـار
He would fin the women bareheaded *** hitting their faces before dawn
قد كن يخبأن الوجـوه تسترًا * * * فاليوم حيـن برزن للنظـار
While they were hiding their face to conceal them *** but today they (openly) show them off to the viewers
Also note that the 3rd war of fijar حرب الفجار between the tribes Kinanah (among them Quraish) and Qays (which have been fought out between 580 and 590 a.D.) started due to an incident where young men of banu Kinanah unveiled a Lady from Qays at the market of 'Okadh.
And in one version of the story of Hatib ibn Abi Balta'ah (here one of three narrations in sahih al-Bukhari) which ibn Kathir quotes in his al-Bidayah wa an-Nihaya apparently quoting ibn Ishaaq shows that the woman whom hid the letter or message was too shy to show off her hair to Ali() and az-Zubayr (and abu Martad who was not mentioned by ibn Kathir and ibn Ishaaq, but in the hadith of al-Bukahri) and said:
فلما رأت الجد منه قالت: أعرض، فأعرض، فحلت قرون رأسها، فاستخرجت الكتاب منها، فدفعته إليه.
(My own translation!)
When she saw that we were determined, she said: turn (yourself) around, turn around, then she opened pigtail and toke the letter out of it and gave it to him.
This shows how much important it was to a free Arab woman not to show off her hair (totally) to foreign men! This incident happened before the revelation of the verse of hijab.
There are many more indications and evidences for the use of a veil by women in Jahilya, but they were not concealing as much as it was later prescribed by the Qur'an as said in:
And abide in your houses and do not display yourselves as [was] the display of the former times of ignorance. ... (33:33)
the used words are وَلَا تَبَرَّجْنَ تَبَرُّجَ الْجَاهِلِيَّةِ الْأُولَى about displaying themselves (tabarruj) as it was the case in the Jahilya, this might be explained by (24:60) where the adornments are referred to as that which shouldn't be displayed (any more). However ibn Kathir seems to disagree, as the ruling for older ladies in this matter has less restrictions!
Ibn Kathir quoted as an explanation for displaying themselves these interpretations:
Mujahid said: "Women used to go out walking in front of men, and this was the Tabarruj of Jahiliyyah.''
(and do not Tabarruj yourselves like the Taburruj of the times of ignorance,)
"When they go out of their homes walking in a shameless and flirtatious manner, and Allah, may He be exalted, forbade that.''
Muqatil bin Hayyan said:
(and do not Tabarruj yourselves like the Tabarruj of the times of ignorance,)
"Tabarruj is when a woman puts a Khimar on her head but does not tie it properly.'' So her necklaces, earrings and neck, and all of that can be seen. This is Tabarruj, and Allah addresses all the women of the believers with regard to Tabarruj. (source qtafsir)
There's also this commentary on verse (33:59) which you may find in ibn Kathir's tafsir explaining the difference between those women who wear rather veiled and those who were not in Medina -which @Kilise has pointed at in a comment:
Muhammad bin Sirin said, "I asked `Ubaydah As-Salmani about the Ayah:
(to draw their Jalabib over their bodies.)
He covered his face and head, with just his left eye showing.''
(That will be better that they should be known so as not to be annoyed. )
means, if they do that, it will be known that they are free, and that they are not servants or whores.
(And Allah is Ever Oft-Forgiving, Most Merciful.)
means, with regard to what happened previously during the days of Jahiliyyah, when they did not have any knowledge about this. (source qtafsir)
Some left out details on the meaning of "That is more suitable that they will be known and not be abused." can be found here in tafsir ibn Kathir (my own translation take it carefully)
إذا فعلن ذلك عرفن أنهن حرائر ، لسن بإماء ولا عواهر ،
this means if they did so they would be recognized as free (neither slaves nor whores).
قال السدي في قوله تعالى : ( [ يا أيها النبي ] قل لأزواجك وبناتك ونساء المؤمنين يدنين عليهن من جلابيبهن ذلك أدنى أن يعرفن فلا يؤذين ) قال :
And as-Suddi said about the meaning of: "O Prophet, tell your wives and your daughters and the women of the believers to bring down over themselves [part] of their outer garments (jilbab). That is more suitable that they will be known and not be abused."
كان ناس من فساق أهل المدينة يخرجون بالليل حين يختلط الظلام إلى طرق المدينة ، يتعرضون للنساء ، وكانت مساكن أهل المدينة ضيقة ، فإذا كان الليل خرج النساء إلى الطرق يقضين حاجتهن ، فكان أولئك الفساق يبتغون ذلك منهن ، فإذا رأوا امرأة عليها جلباب قالوا : هذه حرة ، كفوا عنها .
There have been some wicked people of Medina were going out by night when it becomes dark and "attack" or "molest" women in the streets. As the houses in Medina were narrow the women used to wait until the nights to supply their needs. So these wicked guys were awaiting such circumstances to watch them. So if they saw a woman wearing a jilbab they said: this is a free lady, leave her alone.
وإذا رأوا المرأة ليس عليها جلباب ، قالوا : هذه أمة . فوثبوا إليها .
while if they saw a woman without a jilbab, they said: this is a slave-girl and they went to molest her
وقال مجاهد : يتجلببن فيعلم أنهن حرائر ، فلا يتعرض لهن فاسق بأذى ولا ريبة .
And Mujahid said: they were a jilbab so that they would be recognized as free women and don't be molested by any wicked person without any harm nor doubt.
Note that as-Suddi is not that trustworthy, maybe that's why you may not find this statement in many other classical tafssirs such as at-Tabari or al-Qurtobi or al-Baghawi, however at-Taher Benachour in his tahrir wa-tanwir confirmed that women used to visit the lavatory at night.