With regard to government-owned firm privatization and technology spillovers effect, many papers had investigated before. But the combination of two type of topics, mixed oligopoly and R&D spillover effects ,is unusual. This paper will show how technology spillovers effects markets including both private and public firms. We apply the model of D¡¦Aspremont and Jacquemin (1998) and reassign the objective function of White (1996). In this paper, we present two main results. First, when the commodity is easily replicated due to spillover effect, its production cost must lower. The existence of government-owned firms can higher social welfare and market output. Therefore, government intervention can correct market failure. Second, That government subsidize research cost to public firms can encourage firms to proceed to research and develop. But subsidy cause social welfare reduction under no spillover effect situation. On the contrary, subsidy to public firms higher social welfare in spillover effect situation.