Abstract: In the study of detonation propulsion technology, it is very important to form stable detonation waves for the detonation engine to produce stable thrust. The curvilinear relationship between the angle of oblique detonation and the incoming flow Mach number was determined and the critical Mach number was obtained. The one-step reaction model was used to simulate the oblique detonation with and without viscous diffusion at the near critical Mach number on a large scale. For oblique detonation with a critical Mach number close to C-J characteristics, the simulation results under both viscid and inviscid conditions show that the C-J detonation translates upward in the oblique detonation at critical Mach number.As the oblique detonation stands,its propagation behaves globally oscialltions.