An interparticle contact algorithm based on Riemann solvers and an interpolation method in which the Taylor series incorporates with a kernel estimation are combined to construct a modified smoothed particle hydrodynamic algorithm.Numerical simulations show that the modified algorithm ensures numerical solution accuracy on the boundary and eliminates tensile instability occurred at contact interfaces in impact problemes.It removes numerical compression instability which appears in corrective smoothed particle method (CSPM) as the domain of influence of a kernel function includes many particles or the gradient of the flow is sharp.