The beam divergence effects of the input pump laser on a high power nanosecond optical parametric oscillator (OPO) have been numerically simulated. The OPO conversion efficiency is affected due to the angular deviation of real laser beams from ideal phase matching conditions. Our theoretical model is based on the decomposition of the Gaussian beam and assumes each component has a single deviation angle and thus a Particular wave vector mismatch. We take into account the variable intensity profile in the spatial and temporal domains of the Gaussian beam, the pump depletion effects for large-signal processes as well as the oscillatory effects of the three waves. Two nonlinear crystals β-BaB2O4 (BBO) and LiB3O5 (LBO) have been investigated in detail. The results indicate that the degree of beam divergence strongly influences the maximum pump intensity, optimum crystal length and OPO conversion efficiency.The impact of beam divergence is much more severe in the case of critical phase-matching for BBO than in the case of non-critical phase-matching for LBO. The results provide a way to choose the optimum parameters for a high power ns OPO such as the nonlinear material, the crystal length and the pump intensity, etc. Good agreement is obtained with our experimental results.