The smoothed particle hydrodynamics (SPH) method has the advantage in modeling detonation process. But in most previous applications of SPH method in the simulation of explosives, the detonation process of explosives is usually regarded as steady-state detonation in which the reaction rate of explosive is ignored and propagation of detonation wave is at the Chapman–Jouguet (C–J) state. The simulation of steady-state detonation process cannot predict the von Neumann spike state of explosives which is another important feature in studying condensed explosives. The simulation of condensed explosives response under impact load also cannot base on the steady-state detonation assumption. In this paper, the SPH method is applied to simulate the detonation process of condensed explosives with reaction rate. The ignition and growth model is incorporated into the SPH method to represent the reaction model of condensed explosives. One-dimension detonation process of condensed explosives PBX-9404 and TATB are taken as numerical examples to analyze the feasibility of SPH method in the simulation of detonation with ignition and growth model. Numerical results show that the SPH method combined with ignition and growth model can give good prediction for the von Neumann spike state of detonation in condensed explosives. Propagation and interaction of cylindrically divergent detonation wave in PBX-9404 have also been successfully simulated by SPH method combined with ignition and growth model.