Finite Difference Time Domain(FDTD) method is one of the most active numerical methods applied in the electromagnetic field, which can effectively deal with the scattering of electromagnetic pulses by particles in complex media, as well as the propagation of ultra-wideband electromagnetic pulse in dispersive media. Almost all media, regardless of whether there is absorption spectrum in terahertz(THz) band, may influence the terahertz wave transmission in it. Research of terahertz wave propagation in the media is important for the optimization of terahertz systems, as well as the analysis and design of applied terahertz technologies. This study simulated the terahertz wave transmission in the scattering media, indicating the possibility of adopting terahertz wave in the interferometer for ballistic velocity measurement; and simulated terahertz pulse propagation in dispersive media, providing the basis for crystal selection in terahertz time domain spectroscopy system.