This article presents a three-dimensional (3D) numerical study on rotating detonation engine (RDE), using the premixed stoichiometric hydrogen-air mixture. Different from a conventional numerical setting, intervals are set in the gas intake configuration to bring in effects of nonuniform injection in numerical simulation, which is more semblable to the actual condition in experiments. The simulation successfully shows the spontaneous formation of multiple detonation wave fronts. Discussion is carried out about the factors that affect the phenomenon of multiple detonation wave fronts, which may be helpful to enhance the stability and repeatability of the detonation initiation in RDE experiments. Then subsequently, the simulation result of a typical case is thoroughly described. Three stages of the spontaneous formation of multiple detonation wave fronts after initiation are analyzed. This typical case is also compared to both the conventional simulation and the experimental results to verify its effectiveness.