With the change of climate issues and the needs of economic development, the idea of practicing green and low-carbon behaviors sinks deeper and deeper into people’s hearts. This paper based on the social cost of carbon (SCC) model, this paper constructs a new carbon social cost model by adding the impact of green low-carbon behavior. Classify climate states, based on Bayesian statistical knowledge, study the posterior probability distribution of climate state transitions, and discuss the optimal carbon policy for different climate states by balancing emission utility costs and utility weighted carbon marginal products. This article also discusses the damage caused by rising temperatures and explores their impact on carbon price policies. then, the paper calculates SCC under four kinds of climate states, which will be visually displayed with graphs. Finally, we compare SCC obtained in this paper with that in other researches. The results show that: (1) Climate status has a significant impact on carbon policy, and carbon price predictions will dynamically change with climate status. (2) Green low-carbon behavior has a positive impact on climate status. (3) There are differences in the impact of the three types of damage caused by rising temperatures on carbon price policies. (4) Green development is conducive to stabilizing the value of SCC. (5) Close monitoring of the climate state helps to update the probability of damage in time so that we can precisely adjust the corresponding policies on SCC. This study provides theoretical and empirical reference for the government to formulate carbon price policies and promote the development of social green behavior.