This paper studies a stag hunt game in which each player's payoff depends on the level of social norms in a community. First, we establish conditions under which without social norms, there exists a unique equilibrium regarding the cooperation level, but with social norms, there can be multiple equilibria. Second, we provide the comparative statics analysis such that for a statics framework, the local stability of an interior equilibrium works as a sufficient condition under which the cooperation level increases as the degree of social norms increases; and for a dynamic framework, the cooperation level always increases with social norms.