On the basis of the cost of fear and the strength of refuge on prey species, a stochastic competition models with impulsive effects be formulated. First, by constructing the appropriate Lyapunov function, the existences of a unique global positive solution for the equivalent stochastic system and the stochastic system with impulse are proven. Then, using Itô formula, the stochastic Lyapunov function and some important inequalities, we obtained the sufficient conditions of extinction, non-mean persistence, mean persistence, random persistence and global attraction of system. Finally, through numerical simulation, the impacts of the cost of fear and the strength of refuge, as well as random and impulsive disturbances on predator population were intuitively illustrated.