This thesis explores the China, the United States and the European Union of their domestic or regional policy and stances in international climate negotiations. I borrow the concept of “relative gains” in neo-realism theory and two game models- the Prisoner's Dilemma Game Model and Stag Hunting Model to analyze the cause of the competition in the realm of the climate governance among the three key actors- China, the US and the EU. In order to pursuit relative gains, the three stakeholders have discords in economic and political interests. Besides, the pace and phase of their development is not in accordance to each other and they have different political system and cultural philosophy. Additionally, the international political economy theory and neo-liberal institutionalism are used for the analysis of the present situation and possibility of the international cooperation. The current situation of global climate governance among the three actors is that they are cooperating to promote the mitigation and adaption proceeding of climate change, meanwhile competing with each other. Thus their relationship in climate governance is cooperative, competitive and dynamic, which affects the international mechanism implementation efficiency under UNFCCC and impacts the GHG emission reduction results of global climate governance. The thesis illustrate that because of the deepening cognition and the common interests of all mankind, cooperation under international regimes is possible, but also full of competition at the current stage.