Simulation of surface erosion by impacts of abrasive water-jet is challenging for traditional mesh-based numerical method, because it involves complex phenomena related to fluid-solid interaction, material removal and free surface flows. In this study, the surface erosion mechanism of ductile materials in abrasive water-jet is investigated by using the mesh-free method, smoothed particle hydrodynamics method. In the present SPH model, both the water jet flow and the elastic-plastic target are described by SPH, and the abrasive particle is modeled as the rigid body Our SPH model is improved by combining several corrected algorithms and techniques which helps to increase the stability and the accuracy of the simulation. The artificial density diffusion correction term is introduced in the simulation of water-jet, which reduces the pressure noise. Compared with the method of density re-initialize, the artificial density diffusion correction term is more efficient in pressure noise improvement, making the pressure field more stable. Rigid abrasive particles are discretized with a series of SPH volume particles, and the pressure distribution around the rigid body is improved compared with the previous model of single-layer boundary particles. Kernel gradient correction is used for the water jet flow and the elastic-plastic target respectively to improve the accuracy of numerical simulation. The effect of smoothing length, particle spacing, density correction coefficient and artificial viscosity coefficient on simulation results are also investigated, which provide the basis of the model optimization. The proposed improved SPH model could be useful in the applications of abrasive water-jet machining and metal surface erosion.