Controlling impact dynamics of droplets on solid surfaces is a significant problem in a variety of applications, such as inkjet printing, spray cooling and coating and so on. Most of fluids used in industries always contain various kinds of additives such as surfactants, polymers and particles. Therefore, these fluids exhibit non-Newtonian behaviors, for instance, yield-stress, viscoelastic, shear-thickening and shear-thinning. The impact dynamics of Newtonian droplets on solid surfaces has been extensively investigated. However, the number of researches about fluids with non-Newtonian properties is comparatively very small. In this work, we employ the finite element scheme coupled with level set method to simulate the impact process of droplets on solid surfaces. The numerical simulation models the presence of shear-thinning viscosity by using the truncated power-law rheological model. We first conduct a mesh convergence study and verify the numerical model. The simulation results are found to be in good agreement with experimental data in the literature. By performing extensive numerical simulations and varying the rheological parameters and surface wettabilities, the influences of these parameters on the impact dynamics are evaluated, and the dominant effects that govern the spreading and receding process are determined. The simulation results show that for the case of droplet impacting on surface with contact angle θ = 55°, the spreading is stronger with power-law index decreasing as evidenced by larger shape deformation and faster interface moving speed. As power-law index decreases, we expect the maximum dimensionless diameter to increase and the minimum dimensionless height to decrease during inertial spreading. For the case of droplet with lower power-law index (m = 0.85 and 0.80), which indicates lower viscous dissipation during impact, the dimensionless parameters have significant differences. After first receding, the impacting droplet is not balanced any more and it starts to spread again until its kinetic energy is completely damped by fluid viscous dissipation. For the case of droplet (m = 0.80) impacting on surface, the center breakage can be observed during droplet spreading, which results from the effect of strong shear-thinning property. When a shear-thinning droplet impacts on a surface with contact angle θ = 100°, the oscillation behavior can be observed and the oscillation amplitude increases as power law index decreases. Bouncing phenomenon can be observed when a droplet impacts on surface with contact angle θ = 160°, regardless of rheological property. Finally, we propose an empirical model to predict the maximum dimensionless diameter of shear-thinning droplet impacting on the surface with contact angle θ = 55° as a function of non-Newtonian Reynolds number Re_n.