The financing activities of enterprises are related to the long-term healthy development of enterprises, and when capital becomes the external bottleneck restricting the innovation activities of enterprises, government subsidies will occupy a more critical position in the financing activities of science and technology-based enterprises. In this paper, government subsidies are used as a mediating variable to look at how financing constraints affect different life cycles of science and technology-based businesses. The businesses are then put into four groups: start-up, growth, maturity, and decline. The main goal is to see how financing constraints change during each life cycle. Construct a research model to analyze the relationship between government subsidies, financing constraints, and technology-based enterprises using the mediating variable testing procedure. Combine the sample data to describe the development of innovation activities and the financing status of science- and technology-based enterprises. Benchmark regression analyses are conducted to test the direct effect of government subsidies on the innovation of science and technology-based enterprises, the mediating role of financing constraints, and the heterogeneous effect of the mediating effect of financing constraints under different life cycles, respectively. The analysis shows that the coefficients of government subsidies in the II, V, and X periods are -0.003, -0.006, and 0.056, which are not significant, while the coefficients of government subsidies in VII, VIII, and IX are 0.125, -0.052, and -0.786, respectively, which are significant at the 1% level. It can be seen that the mediation effect of financing constraints under the perspective of government subsidies mainly arises in the maturity period and is not significant in the start-up period, growth period, and decline period.