The fluid saturated porous viscoelastic media is closer to actual stratum than Biot media and single-phase media, and the researches on its dynamic response will be more reliable. In this paper, we proposed a numerical investigation in the time domain of dynamic response on semi-infinite porous saturated viscoelastic medium. An explicit finite element method for dynamic analyses of fluid saturated porous viscoelastic medium was derived on the basis of the classical Biot’s theory with uncoupling technical. Comparing with the conventional implicit methods which need to solve simultaneous equations, our algorithm has the advantages of saving computer memory and computing effort. It achieves satisfying accuracy in contrast with analytical methods. Taking one-dimensional fluid saturated viscoelastic porous medium as example, the influence of viscous coefficient on the dynamic responses has been investigated.