The event of transnational crimes entailed to the reviewing of tradition bases of jurisdiction like territorial and personal jurisdictions. So universal jurisdiction as a legal base for prosecute of international crimes came to internal laws of States. discard with the source and nature of universal jurisdiction, application of universal jurisdiction needs some conditions which can be induced from different sources of international law, like presence of the accused, legality of crime and punishment, dual criminality, awareness of law, Non Bis in Idem principle, et. While there is no doubt in respecting to some of these conditions, there are some challenges to some of them like mutual criminality and necessity of a personal prosecutor. Universal jurisdiction is in conformity with the principle of access to justice and can help to international public order provided respecting to necessary conditions by national courts. Key Words: universal jurisdiction, international criminal law, international law, international crimes, national tribunals.