Many countries use R&D tax credits to promote firm innovation. Using the data of A-share listed companies from 2012 to 2019, we use a fixed effects model to examine the heterogeneity effect of the R&D tax credit in China on radical and incremental innovation based on the perspective of firm property rights, scale, and age under the framework of heterogeneity. The results show that the R&D tax credit significantly stimulates radical and incremental innovation, but the incentive effect on radical innovation is weak. Further heterogeneity analysis shows that the incentive effects of enterprises with different complementary resources and innovation capabilities are different. Specifically, we find that the R&D tax credit has a stronger impact on incremental innovation of state-owned enterprises and radical innovation of non-state-owned enterprises. Compared with small firms and start-ups, it has a stronger incentive effect on the radical and incremental innovation of large-, medium-sized, and incumbent firms. Finally, the results are consistent and robust using the Heckman two-step method, core indicator substitution method, and change lag period. This paper deepens the theoretical research on the heterogeneity effect of tax incentives on firm innovation, while also providing insights on how to design R&D tax credits to raise radical innovation for emerging economies.