The “14th Five-Year Plan” in 2021 calls for “deeply implementing the strategy of strengthening the country through talent, and the strategy of innovation-driven development”. Under the background of Sino-US trade war and technological war, the completion of industrial upgrading through technological innovation is of great significance for China to improve the national innovation system and achieve high-quality development goals. This paper analyzes the impact mechanism of public education investment on innovation ability through the family dynamic education decision-making model, and then selects the panel data of Chinese provinces and cities from 2001 to 2019 for empirical analysis. It uses Sobel and Structural Equation Modeling (SEM) to analyze the mediating transmission mechanism of human capital accumulation. The results show that: (1) Public education investment increases teachers’ wages, increases tuition and miscellaneous fee subsidies, as well as student loan interest subsidies, which will help to lower the income threshold for families to choose education, so that more lower-income families will choose to receive higher education. (2) The Sobel and SEM tests show that increasing public education investment can significantly increase the accumulation of human capital, which can improve the regional innovation capability of the province by increasing the number of employees in the education, R&D and technical service industries. (3) In terms of public education investment channels, increasing teachers’ wages has a greater contribution to the improvement of regional innovation capability than increasing tuition and miscellaneous fees. In addition, public education expenditures have a greater impact on the regional innovation capability than public R&D expenditures. Public education investment in the eastern region is much more effective in enhancing regional innovation than that in other regions. Therefore, public education investment should be tilted towards backward areas and lower-income families, and public education expenditures are increased to subsidize teachers’ wages and tuition and miscellaneous fees. The backward regions in the west should implement supporting policies for educating and retaining talents, so as to strengthen the accumulation of human capital, and promote the implementation of innovation-driven development strategy. The main contributions of this paper are as follows: First, it establishes a theoretical model to analyze how public education investment affects family education decision-making, and how to influence the regional innovation capability by affecting the accumulation of human capital. Second, it analyzes the impact of different channels of public education investment on the regional innovation capability, and compares with the impact of public R&D expenditure on regional innovation.