International crimes such as genocide, crimes against humanity and etc. bring severe effects and disastrous consequences. Subsequently, these are also to the same degree reprehensible, and criminal reaction of states in the form of universal jurisdiction and also responses of the international community in the form of international court with severe punishments are done. Hence, to deal with the question that whether it is possible to exacerbate the punishment of such crimes again in case of the aggravating circumstances or not, we are faced with some uncertainty. Although in terms of philosophy of punish and imposing the penalty, existence of these circumstances for these crimes are imaginable, these circumstances as well as criteria and the resulted intensification of these crimes have received little attention in the context of customary international law and international criminal law. Statute of the Ad hoc international criminal tribunals such as Nuremberg, Former Yugoslavia and Rwanda have no stipulation about these circumstances; however, jurisprudence of two latter tribunals as well as procedure and evidence of ICC discussed this topic relatively but not comprehensively. But still, this question and its criteria and instances, certainly will be one of the most important concerns of ICC jurisprudence in the future. In the meantime, some recognizable of these aggravating circumstances include: extent of brutality and violence in the act committed by international criminals, the social status of criminals, mental state and behavior of criminals after the crime.