Abstract: Based on Euler equations associated with finite-rate chemical reaction mechanism of hydrogen/air mixtures, numerical calculations were performed by using a fifth-order WENO-PPM5 scheme for spatial discretization to simulate the rotating detonation in an annular chamber. Results show that under specific condition, the rotating detonation wave can propagate in two different modes, i.e. single-wave mode and double-wave mode. Comparison was made between the two modes, including the characteristic of flowfield, the feature of detonation propagation, the propulsion performance. Under the same condition, the circumferential velocity of detonation propagation in two modes is approximately equal, and the frequency of double-wave mode is twice as that of single-wave mode; the time-averaged mass flux, specific impulse and thrust of double-wave mode are all a little higher than that of single-wave mode. The height of fresh mixture in two-wave mode is about a half of that in single-wave mode, which is favorable to shorten the length of rotating detonation engine.