A class of Riemann solver-free high resolution schemes with staggered grids for the compution of solutions of systems of hyperbolic conservation laws in two dimensions are presented. Because of Riemann solver-free, no complete set of eigenvectors is needed and hence weakly hyperbolic systems can be solved with much simpler programming. The nu merical results obtained under environment of MPI for parallel computation of these schemes for Euler equation and shallow water equation are satisfied.