We explore R&D subsidies in a hybrid growth model which may exhibit semi-endogenous growth or fully endogenous growth. We consider two types of subsidies on variety-expanding innovation and quality-improving innovation. R&D subsidies on quality-improving innovation only have effects in the fully endogenous-growth regime, in which more subsidies cause an earlier activation of quality-improving innovation and increase the transitional/steady-state growth rate. R&D subsidies on variety-expanding innovation have contrasting effects in the two regimes. In the semi-endogenous-growth regime, more subsidies on variety-expanding innovation increase transitional growth but have no effect on steady-state growth. In the fully endogenous-growth regime, more subsidies on variety-expanding innovation continue to increase short-run growth but delay the activation of quality-improving innovation and reduce long-run growth. Increasing subsidies on variety-expanding (quality-improving) innovation makes the semi-endogenous-growth (fully endogenous-growth) regime more likely to emerge. Finally, we calibrate the model and find that under reasonable parameter values, the fully endogenous-growth regime is more likely to emerge.