Aceh's customary law is customary law that refers to the provisions of the Qur'an and Hadith. Aceh's customary law has been in effect since December 19, 2000, to prevent the separation of Aceh from the Republic of Indonesia where the turmoil of the Free Aceh Movement has reached its peak. But with the enactment of Islamic sharia law in Aceh, got a lot of reactions from the community. The pros and cons of this problem continue to be raised by the community who think that this action includes social discrimination against non-Muslim communities in Aceh. This discussion will explain how the Aceh government implements its customary law without any act of social discrimination. At the end of the discussion, it will be concluded that non-Muslim citizens will still be subject to these regulations if their actions are not regulated in national law or the Criminal Code.