The problem of high costs caused by information asymmetry has limited the development of green supply chain finance. Blockchain, with its unique technical characteristics, has the potential for innovative breakthroughs in financing costs. Starting from the cost perspective, we sort out the operation mode of green supply chain finance empowered by blockchain, analyze the strategic behaviors of green small and medium-sized enterprises (SMEs), core enterprises, and financial institutions, construct a three-party evolutionary game model of green supply chain finance empowered by blockchain, solve the model and discuss the equilibrium of the game, and further simulate and analyze the game by using MATLAB. It is found that the higher the proportion of initial positive strategies of the three parties involved in the game, the higher the probability that the game system will evolve to the Pareto optimal state. Blockchain empowerment makes the financing cost of green SMEs and the evaluation and supervision cost of core enterprises and financial institutions greatly reduced. The cost reduction can prompt the evolution direction of the game system from the Pareto worst state to the Pareto optimal state, and with the increasing cost reduction, the rate of convergence of the game subject to the Pareto optimal stable state increases. The improvement of the autonomous repayment rate of green SMEs has a better role in promoting the credit business and the stable development of green supply chain finance.