Bangladesh is recently prosecuting and punishing the perpetrators of crimes against humanity and genocide committed in the Liberation War of 1971 via a domestically operated International Crimes Tribunal Bangladesh (‘ICTB’). Though the Tribunal is preceded under the municipal law, it's material jurisdiction, i.e., crimes against humanity and genocide are originated from international criminal law. Therefore, this study purposes to examine several legal obligations of the ICTB in defining crimes against humanity and genocide as the core international crimes. Firstly, I scrutinize what is the legal status of international law (treaty and customary law) in Bangladesh's legal system? Secondly, by applying international criminal law standards, I focus on that is it one of the obligations of Bangladesh to apply international criminal law definitions of genocide under the treaty obligation as the contracting parties to Genocide Convention 1948, and the ICC Statute 1998? Thirdly, I also discuss whether Bangladesh has any obligation to apply customary international law definitions of crimes against humanity because crimes against humanity are considered as jus cogens offense in general international law, from which no derogation is permitted. Lastly, after a critical evaluation of domestic and international criminal law instruments, I conclude that Bangladesh certainly failed to fulfill its legal obligation to define international crimes under a treaty and customary laws, which is one of the fatal errors of the ICTB, a government-sponsored criminal tribunal, to secure criminal justice to the accused.