Abstract:DGFEM (Discontinuous Galerkin Finite Element Method) proposes the good abilities in seizing the discontinuous of wave front and eliminating spurious numerical oscillations in structural dynamics and wave propagation problems under high frequency and strong dynamic with comparison to the traditional time-stepping algorithm. But DGFEM, still, bring the spurious numerical oscillations in wave-front. The present paper develops a new version of modified DGFEM by introducing artificial damping term. Numerical simulations illustrate good performance of the present method in eliminating spurious numerical oscillations of wave-front and in reducing the problem of mesh dependence in DGFEM.