The actual seafloor is the typical viscoelastic medium, covered with unconsolidated geological bodies like sand, gravel, sludge, and detritus on the surface. When the seismic wave is propagating therein, viscosity of the seafloor strata will cause seismic wave energy loss, amplitude attenuation and gradual frequency reduction at the wavelet center, and then the accurate subsurface information and high-resolution images cannot be obtained directly from the seismic data due to the reduced signal resolution and SNR. Considering seabed viscoelastic media properties, a model including quality factor, density, and other physical parameters, the flux corrected transport (FCT) algorithm is established to describe the target seafloor and solve the wave equation, in which, the finite difference numerical simulation method of FCT is used to suppress the numerical dispersion generated by differential calculation in coarse grid, improve the seismic wavefield simulation accuracy and computational efficiency. Based on the submarine ancient channel types and the basic characteristics of the real and typical marine geological phenomena, the seismic responses to the three types of submarine ancient channel models, which are straight, curved and braided, are calculated, with good results acquired.