A hydrogen fuel is expected to expand its demand in the future. However, hydrogen has to be treated with enough caution because of wide combustible conditions and easiness to ignite. Detonation accidents are caused in hydrogengas such as the explosion accident in Fukushima first nuclear plant (2011). Therefore, it is necessary to comprehend initiation conditions of detonation to prevent its detonation explosion. In the present study, cylindrical detonationinduced by direct initiation is simulated to understandthe dependency ofequivalence ratios in hydrogen-oxygen mixture.The several detailed kinetic models are compared to select the most appropriate model for detonation in a wide range of equivalence ratios.The Petersen-Hanson model is used in the present study due to the best agreement among the other models. In the numerical results of cylindrical detonation induced by direct initiation, a cellular structure, which is similarto the experimental smoked foil record, is observed. The local pressure is up to 12 MPa under the condition at the standard state.The ignition process of cylindrical detonation has two stages. At the first stage, the normalized cell width, L1/2, at each equivalence ratio increases linearly. At the second stage, cell bifurcations appear due to a generation of new transverse waves.It is observed that a transverse wave transforms to a transverse detonationat the end of the first stage, and after that, some disturbance is developed to be a new transverse wave at the beginning of the second stage.