Abstract: Hamiltonian system with quasi-particles for spatial discrete of acoustic wave propogation is presented. A modified symplectic scheme for temporal discretization of wave equation is proposed. First, we transformed the wave equation into a Hamilton system. An explicit symplecitc Partitioned Runge-Kutta (PRK) scheme is used to solve the Hamilton system. Then, the additional spatial discretization term is added into the symplectic PRK scheme. Theoretical analytic shows the new scheme has lower dispersion and long-term calculation ability than that of the conventional symplectic schemes. Numerical results indicate that the present method is effective and feasible, such as the low numerical dispersion, high stability and long-time performance of the new scheme.