Innovation is a major proposition in today's era. Firms continue to innovate to enhance their competitiveness in the market, but have been prompted to seek R&D cooperation due to the increasing expenses and output uncertainty in R&D. This paper explores the motivation for R&D cooperation between leader and follower firms with technological spillovers, highlighting the impact of R&D cooperation on firms’ market power, total R&D investment of industry and social welfare, and discusses how the government can maximize the social welfare at different spillover levels. This article builds a three-stage dynamic game model: both the leader and the follower decide whether to establish R&D cooperation in the first stage, choose the R&D level in the second stage, and conduct sequential production competition in the third stage. We show that first, unlike the result of static games, in sequential production competition, only when the spillover level is within a relatively low range, the leader and the follower will establish R&D cooperation; second, the R&D cooperation may reduce the market power of leaders; in the end, the market outcomes may be not Pareto efficient. Thus, the research provides a theoretical basis for the government to formulate relevant policies.