Abstract: Government investment in basic research and applied research was introduced into Romer’s innovation-driven growth model. By solving general equilibrium and numerical simulation, it finds that government investment in basic research has greater effect on sustainable economic growth than that in applied research. In addition, it explored the Dynamic impact relationship among government investment in basic research and applied research and economic growth with data of 1991-2015 through time series Var model. The results show that firstly government investment in applied research has greater effect on short-term economic growth, but the effect on long-term economic growth by government investment in basic research is much greater. Secondly, maximizing the promotion to economic growth, government investment in applied research needs 5 periods, but government investment in basic research needs 8 periods, so government investment in basic research take longer to play the extreme positive role. Thirdly, government investment in basic research not only promote economic growth directly, but also drive government investment in applied research to promote economic growth indirectly. That is to say government investment in basic research is the engine of economic growth. Such findings provide theoretical and empirical foundation for government R&D policy-making scientifically.