Accurate analysis of seismic wave propagation in coal and rock media can provide theoretical basis for coal mine seismic exploration and inversion. In this paper, based on the theory of isotropy and anisotropy, the single homogeneous media model of coal and rock, the two-layer and three-layer media model of coal and rock are established. The pseudo spectral method is used to simulate the wave field and analyze the wave field characteristics under different models. The results show that: (1) in the two-layer and three-layer coal rock media model, the wave will reflect and transform in the coal and rock media layer, and generate reflection wave, transmission wave, reflection converted wave and transmission converted wave. At the coal-rock interface, the amplitude of reflected wave generated by P-wave is greater than transmission wave, and for S-wave, the amplitude of reflected wave is smaller than transmission wave; (2) when the wave propagates from rock stratum to coal seam, the wave velocity of reflected wave and reflected converted wave is greater than transmission wave and transmission converted wave, and the wave front presents a diamond shape with width at the top and flat at the bottom. When the wave propagates from the coal seam to the rock stratum, the wave front shape is opposite; (3) whether the wave is incident from the coal seam to the rock layer or from the rock layer to the coal seam, the reflected wave velocity is faster than the corresponding reflection converted wave, and the transmission wave is greater than the transmission converted wave; (4) for anisotropic medium, the wave front is no longer circular, but has the characteristics of ellipse, and the wave field appears qP Wave and qSV wave, which makes the wave field more complex.