Climate change has caused serious threats to global economic development and human well-being, and green finance is a new way to achieve ecological, economic, and social sustainable development, and it also has important theoretical significance and policy value. This study firstly aims to study the impact of green finance on regional carbon intensity. Then, it aims to determine the moderating effect of capital stock per capita on the relationship between green finance and carbon intensity based on moderating effect model as well as to investigate the threshold effect of capital stock per capita on the relationship between green finance and carbon intensity based on threshold effect model. The main conclusions are as follows: (1) Every 1% increase in green finance will lead to a 2% decrease in carbon intensity, and the inhibition of green finance on carbon intensity is most obvious in northeast and east China. (2) The capital stock per capita has a significant moderating effect, which could enhance the restraining effect of green financial development on carbon intensity, and this moderating effect is most obvious in northeast China. (3) The capital stock per capita has a threshold effect in the process of green finance development to suppress carbon intensity. The higher the capital stock per capita, the stronger the inhibition effect of green finance development on carbon intensity. Therefore, in the process of capital accumulation, attention should be paid to improve the relevant legal system and policy guarantee, optimization of financial structure, and stimulation of the capital allocation effect of green finance. Simultaneously, in order to strengthen the inhibitory effect of green finance on carbon intensity, differentiated green finance development policies should be formulated based on factor endowment structure and comparative advantages of different regions.