In this paper, the pressure stabilization method of the stochastic Navier-Stokes equation with multiplicative noise is studied, and the velocity pressure space is approximated by first-order finite elements. This method solves the problem of finite element space pair selection by introducing stabilization parameters and decoupling velocity pressure variables. The stability and convergence of the pressure stabilization method are proved theoretically. Finally, it is proved that the convergence order of space discreteness can reach the optimal when the stabilization parameters meet certain conditions.