We develop a new dynamic earthquake simulator to numerically simulate both spontaneous rupture and aseismic slip over earthquake cycles on geometrically complex fault systems governed by rate‐ and state‐dependent friction. The method is based on the dynamic finite‐element method (FEM) EQdyna, which is directly used in the simulator for modeling 3D spontaneous rupture. We apply an adaptive dynamic relaxation technique and a variable time stepping scheme to EQdyna to model the quasi‐static processes of an earthquake cycle, including the postseismic, interseismic, and nucleation processes. Therefore, the dynamic and quasi‐static processes of an earthquake cycle are modeled in one FEM framework. Tests on a vertical strike‐slip fault verify the correctness of the dynamic simulator. We apply the simulator to thrust faults with various dipping angles, which can be considered as the simplest case of geometrically complex faults by breaking symmetry, compared with vertical faults, to examine effects of dipping fault geometry on earthquake cycle behaviors. We find that shallower dipping thrust faults produce larger seismic slip and longer recurrence time over earthquake cycles with the same rupture area. In addition, we find an empirically linear scaling relation between the recurrence interval (and the seismic moment) and the sinusoidal function of the dip angle. The dip‐angle dependence is likely due to the free‐surface effect, because of broken symmetry. These results suggest dynamic earthquake simulators that can handle nonvertical dipping fault geometry are needed for subduction‐zone earthquake studies.