In recent years, along with the growing demands for accuracy and efficiency in numerical simulation of seismic wave-field, discontinuous finite element methods begin to attract more and more attentions. In this paper, a numerical simulating algorithm based on local discontinuous Galerkin method is proposed for the 2-D seismic acoustic wave equation, which is imposed on by an absorbing boundary condition. In this algorithm, local discontinuous Galerkin method is applied to spatial discretization, while explicit Leap-Frog method is used for temporal discretization. With this combined pattern, computational process on every spatial element is independent of each other, which causes the algorithm to be highly parallelizable. Numerical experiments, in which this algorithm is compared with continuous finite element method, indicate that this algorithm not only obtains preferable simulation effect when dealing with rugged topography, but also has advantages over continuous finite element method in computational efficiency and accuracy.