To realize green, low-carbon, and high-quality development, scientific and technological innovation is the key, but green technological innovation is costly and risky, and the effectiveness of single-principle innovation is very low. The green technology innovation ecosystem led by the government, supported by financial institutions, and with enterprises as the main body of innovation can provide policy leadership, financial guarantee, and technical support for green technology innovation, share the risk of green technology innovation on a single subject, and promote the rapid generation of green science and technology innovation results and their transformation into benefits. However, the stability of the system platform is constrained by the influence of a variety of factors, in order to promote the development of green technological innovation and to ensure the stable development of the system, this paper explores the government, financial institutions and enterprises tripartite green science and technology innovation system, establishes the tripartite evolutionary game model, and adopts numerical simulation methods to carry out the stability analysis of the system, and the results of the study show that: (1) the stability of government, financial institutions and enterprises of green science and technology co-innovation is subsidized by the government’s policy guidance, innovation benefits, high-end greenness of technology, technology spillover and other factors，strong governmental guidance on the willingness of financial institutions and enterprises to cooperate; (2) financial institutions synergistic strategy is susceptible to external factors, financial institutions subsidies to enterprises should be assessed according to the benefits of technology, degree of difficulty and the ability of enterprises; (3) the greener and higher-end technological innovations, the more the main body of each party will protect the technology, the higher the exit cost, the higher the synergistic innovation bundles; (4) the risk of green technology spillover risk is high and has a greater impact on the stability of collaborative innovation, the government should establish corresponding laws and regulations to protect intellectual property right.