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With the world population growth, energy consumption and the rapid development of industrial economy, a large amount of carbon emissions has brought destruction and threats to the earth's environment on which human beings depend. The development of low-carbon economy has become the consensus of governments all over the world and has been vigorously advocated & promoted. This paper focuses on the top five global GDP nations in 2022: The United States, China, Japan, Germany, and Britain. A comprehensive evaluation index system of urban low-carbon economic development level is constructed from four dimensions: economic development level, environmental quality, energy consumption emission intensity and social development speed by using literature review and field interview. The evaluation measures are determined using the TOPSIS evaluation method with entropy weight and the grey relational model, providing a comprehensive assessment of the low-carbon economy's development level in these five countries." Judging from the comprehensive evaluation score, the overall development of low-carbon economy in American cities is in good condition and has reached the development standard of low-carbon economy; Germany and Japan rank second and third, and they are low-carbon economies. Britain ranks fourth in comprehensive evaluation, although it belongs to a low-carbon economy country, but there is still a certain gap with Germany and Japan; There is still a big gap between China and the other four countries. Based on the measurement and evaluation outcomes, it presents recommendations and strategies to foster the growth of low-carbon economies, offering valuable insights for the advancement of such economies across different nations. The research results guide countries all over the world to reduce carbon emissions in the process of economic development, protect the earth environment on which human beings depend, and make a better tomorrow for sustainable development. [ABSTRACT FROM AUTHOR]