Abstract: The extreme transient of underwater explosion possesses dynamically extreme characteristics with extremely large deformation and large in homogeneity，which bring a lot of dificulties to the investigation using conventionally grid-based numerical simulation methods． A mesh free smoothed particle hydrodynamics(SPH)method is applied to simulate the detonation process of underwater explosion．The simulation results show that SPH method can give a very good prediction for both the magnitude and the shape of the detonation waves as well as the pressure distributions in the detonation process．Consequently，the SPH method is suitable for solving problems with dynamically extreme characteristics with extremely large deformation and large in homogeneity of underwater explosion，and it provides a new method for further numerical simulation of underw ater explosion．