As an effective measure for the local government to promote reduction of corporate carbon emissions and sustainable development of social economy, the implementation of green finance policies in enterprises and financial institutions has encountered severe strikes from the low returns of low carbon production and low interest rates of green credit business. Under the premise of liberalizing carbon emissions trading, a triple‐level network evolutionary game consisting of a local government, banks, and enterprises is constructed to analyze response behavior and strategy selection mechanism to green credit. The impacts of management tools are investigated in terms of setting carbon market price, limiting the financing upper bound of misbehaving enterprises, limiting the emissions quota of enterprises for fraudulent green credit, and rewarding clean project development on the decisions of individuals in the network. Results show the following: First, increasing the trading price of carbon emissions has a catalytic effect on enhancing the activeness of banks and enterprises to follow green finance policies, but the autonomous regulation ability of which is limited. Second, reducing the funding ceiling for emitting emissions illegally ambiguates enterprises' preferences for production strategies and discourages them from undertaking low‐carbon projects. Third, excessive restrictions on the share of emissions may evoke regulatory inaction by the local government, consequently leading to instability in the evolution network. Fourth, granting reward for clean production is instrumental for the network to promote green finance policies, but exorbitant subsidies increase the fiscal burden of the local government with no significant effect on the node selection of environment‐friendly strategies.