It is important to study seismic wave propagation through fractures in the field of earthquake engineering. Based on elasticity mechanics and wave motion theories, the propagation law of an anti-plane SH-wave across a ground fissure interface is analyzed using time-domain and frequency-domain calculation methods in this paper. Recursion equations are established and a contrast verification between the two methods is conducted. The influence of certain related parameters on the propagation law of anti-plane SH-waves are discussed, including the equivalent shear stiffness of the ground fissure interface, incidence wave frequency, incident angle, and shear strength of the fissure surface. Furthermore, a cross-comparison of these parameters is performed, and recursion equations considering the shear strength of fissure are established. Results indicate that the transmission coefficient increases with an increase in equivalent shear stiffness and the incident angle, but decreases with an increase in incident frequency. In addition, the low-pass filtering effect of the ground fissure interface is more evident with a decrease in equivalent shear stiffness and the incident angle. Under the input of a real seismic wave, there is a decrease of transmission coefficient but no obvious decrease in the amplitude of the transmission wave. However, the waveform change is obvious. The amplitude and wave form of the reflection wave gradually approach the incident wave, but the effect of hysteresis occurs in the phase relative to incident wave. To obtain an effective and real propagation law of wave motion, fluctuation time-history data were processed using linear interpolation, and results indicate that there are no changes to the precision of calculation results using this method.