Just is one of the 99 names of God in Islam. God is just and wants us to be just. This is well spelled in both the Bible and Quran. Please examine the verses in Quran that talks about justice.
1- God himself is standing firm on justice: 3:18 There is no God but He: That is the witness of Allah, His angels, and those endued with knowledge, standing firm on justice. There is No God but He, the Exalted in Power, the Wise. شَهِدَ اللّهُ أَنَّهُ لاَ إِلَـهَ إِلاَّ هُوَ وَالْمَلاَئِكَةُ وَأُوْلُواْ الْعِلْمِ قَآئِمَاً بِالْقِسْطِ لاَ إِلَـهَ إِلاَّ هُوَ الْعَزِيزُ الْحَكِيمُ
2- The failure of seeing complete justice in our world requires an afterlife for real justice (Which for our good luck is real): 3:25 But how (will they fare) when we gather them together against a day about which there is no doubt, and each soul will be paid out just what it has earned, without (favor or) injustice
فَكَيْفَ إِذَا جَمَعْنَاهُمْ لِيَوْمٍ لاَّ رَيْبَ فِيهِ وَوُفِّيَتْ كُلُّ نَفْسٍ مَّا كَسَبَتْ وَهُمْ لاَ يُظْلَمُونَ
3- God is just he gives us signs of his existence: 3:108 These are the Signs of Allah. We rehearse them to thee in Truth: And Allah means no injustice to any of His creatures. تِلْكَ آيَاتُ اللّهِ نَتْلُوهَا عَلَيْكَ بِالْحَقِّ وَمَا اللّهُ يُرِيدُ ظُلْمًا لِّلْعَالَمِينَ (in another verse: We would not torture (people) until we send a messanger.). Both the Bible and Quran have the words of God.
4- Unlike most of non-Muslims belief justice in marriage requires the norm to be one wife. In the verse marrying more than one woman was mainly to support the orphans (The right hands possess are like slaves that Islam managed to put mechanisms to free them): 4:3 If ye fear that ye shall not be able to deal justly with the orphans, Marry women of your choice, Two or three or four; but if ye fear that ye shall not be able to deal justly (with them), then only one, or (a captive) that your right hands possess, that will be more suitable, to prevent you from doing injustice.
وَإِنْ خِفْتُمْ أَلاَّ تُقْسِطُواْ فِي الْيَتَامَى فَانكِحُواْ مَا طَابَ لَكُم مِّنَ النِّسَاء مَثْنَى وَثُلاَثَ وَرُبَاعَ فَإِنْ خِفْتُمْ أَلاَّ تَعْدِلُواْ فَوَاحِدَةً أَوْ مَا مَلَكَتْ أَيْمَانُكُمْ ذَلِكَ أَدْنَى أَلاَّ تَعُولُواْ
5- Even being generous has to have a balance. You need to be just to yourself when you give out: 4:5 To those weak of understanding Make not over your property, which Allah hath made a means of support for you, but feed and clothe them therewith, and speak to them words of kindness and justice.
وَلاَ تُؤْتُواْ السُّفَهَاء أَمْوَالَكُمُ الَّتِي جَعَلَ اللّهُ لَكُمْ قِيَاماً وَارْزُقُوهُمْ فِيهَا وَاكْسُوهُمْ وَقُولُواْ لَهُمْ قَوْلاً مَّعْرُوفًا
6- To be honest and to judge with justice are God commands: 4:58 Allah doth command you to render back your Trusts to those to whom they are due; And when ye judge between man and man, that ye judge with justice: Verily how excellent is the teaching which He giveth you! For Allah is He Who heareth and seeth all things. إِنَّ اللّهَ يَأْمُرُكُمْ أَن تُؤدُّواْ الأَمَانَاتِ إِلَى أَهْلِهَا وَإِذَا حَكَمْتُم بَيْنَ النَّاسِ أَن تَحْكُمُواْ بِالْعَدْلِ إِنَّ اللّهَ نِعِمَّا يَعِظُكُم بِهِ إِنَّ اللّهَ كَانَ سَمِيعًا بَصِيرًا
7- God is just if we are righteous we will enter heaven (but we have to be believers, it is unjust to deny God and he would recognize you): 4:124 If any do deeds of righteousness,- be they male or female - and have faith, they will enter Heaven, and not the least injustice will be done to them. وَمَن يَعْمَلْ مِنَ الصَّالِحَاتَ مِن ذَكَرٍ أَوْ أُنثَى وَهُوَ مُؤْمِنٌ فَأُوْلَـئِكَ يَدْخُلُونَ الْجَنَّةَ وَلاَ يُظْلَمُونَ نَقِيرًا
8- In fact the Quran is true and just and no change of its words for over 1400 years: 6:115 The word of thy Lord doth find its fulfillment in truth and in justice: None can change His words: for He is the one who heareth and knoweth all.
وَتَمَّتْ كَلِمَتُ رَبِّكَ صِدْقًا وَعَدْلاً لاَّ مُبَدِّلِ لِكَلِمَاتِهِ وَهُوَ السَّمِيعُ الْعَلِيمُ
Verses are collected from www.islamicity.com Translation of Quran to Yusuf Ali.