Earthquakes are one of the most significant external factors that induce the failure of anti-dip bedding rock slopes (ABRSs). The pseudo-static method is currently (and is likely to remain in the near future) the most effective and popular method used to evaluate the stability and design of such slopes under the action of earthquakes. In this work, based on the limit equilibrium method and genetic algorithm, a new method considering the inertial force of earthquakes is proposed to assess the stability of ABRSs. Results previously obtained from centrifuge tests and reported in the literature were used to investigate the veracity of the proposed method. A parametric study was then performed to investigate the effects of earthquakes and the mechanical properties of the rock layers on the failure mechanism of an ABRS. The results show that ABRSs are more likely to undergo a complex combination of shearing and flexural toppling failure under the combined action of gravity and earthquake. The direction of the earthquake-induced inertial force, tensile strength of the rock layers, and shear strength of the joints significantly affect the stability of ABRSs. On the other hand, these factors have little influence on the shape of the failure surface. The failure surface is stepped (with steps of different heights) rather than a plane. The failure surface and corresponding safety factor of an ABRS can be readily found using the proposed method, and the failure mode of each rock layer can be obtained. The method proposed in this work provides a convenient theoretical tool for the design of ABRSs in regions prone to seismic activity.