Porous materials are ubiquitous in the subsurface formations of the earth where acoustic and seismic waves are used for remote sensing. However, it is not well understood how the dissipation and the dispersion of poroelastic waves are caused by the viscoelastic and viscous properties of the constituents such as solid grains and pore fluid and by the viscoelastic dissipation of the solid frame, as well as the viscodynamic coupling of the pore fluid to the solid frame due to its global and local flows relative to the solid grains. Such attenuation mechanisms have seldom been incorporated in subsurface sensing simulations, although they can be very important to applications. In this paper, we propose a complete attenuation model, including both full stiffness and viscodynamic dissipation, for poroelastic media in seismic wave simulations. Completely based on a generalized Zener model, the effects associated with physical dissipation and frequency-dependent dispersion are accurately simulated by a finite-difference time-domain algorithm. Verifications with analytical solutions show the accuracy, efficiency, and flexibility of our method. Numerical results demonstrate that the attenuation of Biot's model in the sediment of the seafloor has significant effects on acoustic wave scattering from complex geologic structures.