In this paper, three-dimensional numerical simulations are performed to investigate the formation and propagation characteristics of rotating detonation wave in a non-premixed engine. By changing the mass flow rate of H-2 and fixing air mass flow rate, the effects of equivalence ratio involving fuel lean and rich operating conditions are mainly discussed. Numerical results show that equivalence ratio plays a very critical role in the formation process and propagation mode, which further affects the propulsion performance of rotating detonation engine significantly. For current numerical geometry and operating conditions, the lean limit of equivalence ratio for formatting a stable RDW is about 0.4, dual-wave mode (at equivalence ratio of 0.6, 0.8, 1.0 and 1.4) and single-wave mode (at equivalence ratio of 1.2) are obtained, respectively. When equivalence ratio is 1.0, rotating detonation engine can exhibit excellent operating performance with the shortest formation time, best propagation stability, middling class thrust and specific impulse. Besides, the pressure contour analysis indicates that the effects of equivalence ratio and mass flow rate of H-2 on the collision strength and times during the re-initiation process are the main mechanisms for determining the formation possibility and propagation mode of rotating detonation wave. Besides, the intensity of accumulated pressure wave and distributions of equivalence ratio are two important factors for the generation of new detonation wave front. Furthermore, it is also detected from the comparisons of the propulsion performance that the effects of equivalence ratio on thrust and specific impulse under fuel lean conditions are more significant than those under fuel-rich conditions. (C) 2019 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved.