For the low-order finite element pair $P_1-P_1$, based on full domain partition technique, a parallel pressure projection stabilized finite element algorithm for the Stokes equation with nonlinear slip boundary conditions is designed and analyzed. From the definition of the subdifferential, the variational formulation of this equation is the variational inequality problem of the second kind. Each subproblem is a global problem on the composite grid, which is easy to program and implement. The optimal error estimates of the approximate solutions are obtained by theoretical analysis since the appropriate stabilization parameter is chosen. Finally, some numerical results are given to demonstrate the high efficiency of the parallel stabilized finite element algorithm.