To alleviate the job burnout of medical staff and improve their physical and mental health, this study proposes building a hospital gym to solve the problem of physical inactivity of medical staff. With the policy call for a “National Fitness Program” in China as the background, this study established a game model involving hospitals and medical staff in different situations with or without government incentives. An evolutionary game was used to explore the influence of strategy selection, stable equilibrium strategy, and its influencing factors among government, hospital administrators, and medical staff in the construction and use of gyms. The results show that the strategy choice of the government, hospital administrators, and medical staff influenced each other. Specifically, the stronger the willingness of hospitals to build gyms, the more willing medical staff to actively use gyms. The game system has two stable equilibrium strategies: hospitals do not build gyms, the medical staff does not actively use gyms, hospitals build gyms, and medical staff actively use gyms. The government incentive measures promote a stable and balanced strategy towards hospital construction and active use by medical staff. Moreover, many factors involved also have an important impact on the strategy selection of each subject.