Abstract As a permanent international criminal judicial institution, from the day International Criminal Court (ICC) established, it means that the international community will not tolerate serious international crimes any more. Serious international crimes will be punished, even if they are heads of states or officers of the military trips. According to the articles of the Rome Statute of the International Criminal Court, ICC follows the principle of complementary and focus on four of the most serious international crimes, that is genocide, crimes against humanity, war crimes and crimes of aggression and other crimes have jurisdiction over four categories designed to make these most serious crimes impunity for the perpetrators to help prevent these crimes. The establishment of the ICC provides a new guarantee to for the peace and security of the mankind. It is the common well-being for human beings. This thesis will focus on the topic of the jurisdiction of the ICC and take the principle of complementarity as the emphasis of research. Furthermore, we will discuss the relationship between China and ICC. In this thesis, we will analyze the history and the establishment of this court and try to use the historical background explain the jurisdiction of ICC. Then we will discuss basic issues of the ICC, such and the characteristics of the jurisdiction, the crimes under the jurisdiction of the ICC, and the mechanism to start the jurisdiction of the ICC. After that, we will focus on the most important characteristics of the jurisdiction which is the principle in disputes, which is the principle of complementary. In this part, we will discuss the legislation of this principle and the disputes about this principle. Based on the discussion above, we will talk about the relationship between China and of ICC. To analyze the reasons of why China and some important countries in the world refuses to join the International Criminal Court, at the same time go give some feasible proposal for China. Keywords: International Criminal Court; Jurisdiction; Principle of Complementarity; Rome Statute