Abstract: Detailed chemical reaction model and finite volume method are used to numerically investigate detonation direct initiation induced by the toroidal shock wave focusing in combustible gas mixture. Numerical results show that detonation direct initiation will be initiated by toroidal shock wave focusing in the standard hydrogen-air gas mixture if the incident Mach number is above 3.1. Then the detonation wave interacts with shock waves and contact surfaces, which results in complex wave system. The initiation point is not fixed on the focusing point but varies with the incident shock Mach number. The critical Mach number is influenced by the initial pressure and temperature, but the temperature is the main factor.