A high-order CIP(Constrained Interpolation Profile,HCIP) method is developed by constructing a high-order interpolation function based on high-order spatial derivatives.Numerical errors of both HCIP scheme and a standard CIP(SCIP) scheme proposed by Yabe and et al are studied.With HCIP method,we investigate numerically physical problems in the famous Vlasov-Poisson equation,such as Landau damping and two-stream instability.It shows that HCIP method is a fifth-order accuracy scheme.Its accuracy is higher than that of SCIP method.Dynamical evolution due to Landau damping in an electrostatic plasma simulated by HCIP method agrees well with previous results.By reducing the number of grids calculation speed is increased with same accuracy.