Abstract:The influence of innovation on economic growth is mostly discussed in existing research, but rarely involves the discussion of the nonlinear U-shaped law of innovation-driven economic growth, and the role of financial incentives in this law is studied, and corresponding hypotheses are drawn. . The paper selects the balance panel data of 100 countries or regions in the world from 1995 to 2017 to explain the mechanism of this law and carry out tests, through the least squares method (OLS), the two-stage least squares method of instrumental variables (2SLS) , Limited information maximum likelihood method (LIML) that is not sensitive to weak instrumental variables, generalized moment estimation method (GMM) that is more efficient for heteroscedasticity, and iterative generalized moment estimation method (iterative GMM) respectively estimate the model, It tested its possible financial incentive mechanism and its heterogeneity. Through multiple endogenous and robust method tests, it is found that innovation-driven economic growth satisfies the U-shaped law and the financial incentive mechanism has played a leverage role, magnifying the effect of this law and making it more obvious. The policy enlightenment of choosing the target of innovation project appropriately, carrying out reasonable investment, and continuing to support innovation, has some enlightenment for breaking the "income trap" problem.