This paper analyzes the government R&D subsidy strategies at different stages, considering cost efficiency differences and subsidy rate as endogenous variables, and extends the subsidy from symmetric to asymmetric cases. We find that although subsidies in the R&D stage bring greater innovation output, they may lead to a deadweight loss of social welfare, while choosing the optimal subsidy rate in the output stage can maximize social welfare. It’s usually difficult for governments to pursue both maximum social welfare and innovation output. The cost efficiency of R&D and the symmetry of subsidies will also influence the strategies of government subsidy policies.