Taking the advanced technology of the foreign firm into account, a mixed duopoly three-stage game model is established in the context of research and development（RD）investment subsidies and product subsidies for domestic firms provided by the government, and the RD subsidy policy of domestic firms in competition with foreign firms is analyzed.The equilibrium output, RD investment of the domestic firm, social welfare and the value of government subsidies are derived, in the case of the two policies, RD investment subsidies and product subsidies for domestic firms, provided by the government. The results show that, the equilibrium output and the optimal social welfare under the RD investment subsidy policy are both less than those under the product subsidy policy; the optimal RD investment under the RD investment subsidy policy is less than that under the product subsidy policy; and the RD product subsidy has a more obvious incentive effect on firm RD investment. Under the background of the leading edge of technology of foreign firms, the product subsidy policy drawn up by the government to encourage RD innovation of domestic firms is more effective than the RD investment subsidy policy.
