Seismic numerical modeling is a technique for simulating the wave propagation in the earth. The aim is to predict the seismogram, given an assumed structure of the subsurface. Real subsurface structure is complex and often multi-phase media because of fluid saturation, so the commonly used models such as acoustic, elastic media, etc., cannot characterize the information of real subsurface structure. The anelastic attenuation occurs when the waves propagate in fluid-saturated media. The diffusive-viscous model can be used to describe the attenuation of seismic waves propagating in fluid-saturated rocks, and it is also used to investigate the relationship between the frequency dependence of reflections and fluid saturation in a porous medium. In this paper, we derive the finite-difference scheme for the diffusive-viscous wave equation and simulate the propagation of seismic waves in fluid-saturated media based on the diffusive-viscous model, using the flux-corrected transport-finite-difference method (FCT-FDM). The numerical results show that the propagating waves in fluid-saturated media greatly attenuate by comparing with those of acoustic case.