The curvature of the contact line is always changing with the dynamic wetting condition. Using a modified Wilhelmy plate method and the sessile drop method, this study experimentally investigated the dynamic wetting process of several kinds of Newtonian and non-Newtonian fluids. The results show that the curvature of the moving contact line strongly affects the relationship theta(D) = f(U) for non-Newtonian fluids but has no effect on Newtonian fluids. The effect is more obvious with the stronger non-Newtonian fluids. The theoretical relationship derived from the Navier-Stokes equations established for spontaneous spreading indicates that the moving contact line curvature affects the relationship theta(D) = f(U) for shear-thinning fluids and shear-thickening fluids in a different way, which agrees with the forced wetting experimental results for shear-thinning fluids in both this work and the previous one on the fluid showing shear-thickening rheology. A force balance relation of the braking force and driving force for the moving contact line is used to explain the internal mechanism about how the curvature of the contact line affects theta(D) during wetting process.