Oblique detonation waves in hydrogen-air mixtures are simulated with detailed chemical reaction models to study the initiation process. To mimic the flow in Oblique Detonation Wave Engines (ODWE), the combustible gas mixtures, with low pressure and high temperature, are derived from flight condition and used in the simulations. Numerical results show the initiation is achieved through the smooth transition from oblique shock to detonation, different from the abrupt transition studied widely before. The mechanism of forming the smooth transition is discussed, which is consistent with previous theory. To perform quantitative analysis, the characteristic length of initiation process is defined, and then the length dependences on detonation-induced wedge angle, incident Ma and flight Ma are listed.