Under the goal of carbon peaking and carbon neutrality，the development of carbon finance is an important driving force for the continuous and vigorous development of the carbon market and a key part of the realization of the two-carbon goal. This paper first reviews the origin of carbon finance and defines the concept of carbon finance. Secondly，it expounds on the development of the carbon finance system from both international and domestic aspects.The analysis finds that in the international aspect，carbon trading in the European Union is increasingly popular，and its internal development is quite different. Germany and the Netherlands actively promote carbon finance by establishing funds and improving relevant regulatory mechanisms，and carbon finance develops rapidly. North America has rich experience in carbon financial product innovation and institutional design，and actively encourages private sector participation. The UK，Japan，and New Zealand are also actively involved in carbon finance practices.At the same time，social organizations and international organizations are also important drivers for actively promoting the innovation and development of carbon finance. In the domestic aspect，the pilot carbon market has good practices in carbon financial instruments such as carbon emission right pledge loan，carbon bond，carbon emission right long-term，carbon index，and carbon fund，among which Hubei region has played an important role in promoting the development of carbon finance. The development of the regional carbon market has laid a good foundation for the national carbon market finance，but at the same time，it puts forward higher requirements for risk prevention and control. Finally，based on the analysis of the international and domestic status quo，the development trend of China’s carbon market is predicted and prospected.