Critical parameters of detonation direct initiation are important to the utilization of detonation and the safety of industrial process. The model of detonation direct initiation was established, as shown in the figure in abstract and a criterion for spherical detonation direct initiation was put forward based on ZND theory of detonation wave structure and theory of strong point blast. The critical radius of detonation kernel and the critical energy of spherical detonation direct initiation can be calculated by using the basic properties of gaseous mixture. The critical radius of detonation kernel and the critical energy of spherical detonation direct initiation in hydrogen/oxygen mixtures were studied. The influences of equivalence ratio and initial pressure on the critical parameters of spherical detonation direct initiation were investigated. The calculated critical energy of spherical detonation direct initiation in hydrogen/oxygen mixtures was compared with the experiment result and reasonable agreement was obtained. Copyright (C) 2015, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights reserved.