The Measurement,Reporting and Verification (MRV) of climate finance was originated from the United Nations Framework Convention on Climate Change (UNFCCC). It has been one of the key issues of global climate negotiations since 2009 and will continue to be of significant importance in addressing climate change and strengthening international trust. The decision of biennially communicate' agreed in Paris Agreement will strengthen and improve the MRV of climate finance. This paper analyses the concept, the objective and the updated progress of the MRV of climate finance based on review of the updated literatures and think-tank reports regarding climate finance mechanisms and MRV. The paper also illustrates the challenges faced with the MRV under the UNFCCC. The paper presents that the comparability of climate finance data needs to be improved due to the varieties of climate finance classifications used by different statistics and accounting organizations. Moreover, the integrality of the MRV system of climate finance has been impaired by the lack of feedback mechanism from the recipients to the contributors. Although the accounting system of climate finance is developing and improving, it remains incapacity in providing accurate data of climate finance disbursement. Responding to the above challenges,this paper proposes the key tasks in establishing a comprehensive international MRV system of climate finance. The tasks involve developing a measurement system of climate finance with consistent data basis and accounting basis, a reporting system with more detailed guidance and more standardized formats,as well as verification mechanisms balancing top-down and bottom-up verification processes. In the last section, this paper concludes that the construction of an international MRV system of climate finance requires the cooperation and negotiations between developed Parties and developing Parties under the UNFCCC. As one of the few developing donors to Global Environmental Facility, it is suggested that China clarify the propositions of developing Parties in climate finance attributes,key concept and coverage of the MRV mechanism,and make effort in influencing the operating and technical rules of international climate finance mechanisms.