The smoothed particle hydrodynamics (SPH), as a fully Lagrangian particle method, has been suc- cessfully applied to astrophysical problems and extended to elastic dynamics and computational fluid dynamics. High order derivatives have to be approximated when elastic dynamics problems are modeled. However, the approximation errors in SPH could lead to computational failure in the case that the order of derivative is high. A novel method was proposed in order to improve the accuracy of SPH method, which shows the relationship between the selected functions and their SPH approximations. The entire involved system was represented by a finite number of particles that carry individual mass and occupy individual space, and the integral interpo- lation was approximated by a summation interpolation. In addition, error comparison was made between SPH method with and without the present improvement. The smoothed particle hydrodynamics (SPH), as a fully Lagrangian particle method, has been suc- cessfully applied to astrophysical problems and extended to elastic dynamics and computational fluid dynamics. However, the approximation errors in SPH could lead to computational failure in the case that the order of derivative is high. A novel method was proposed in order to improve the accuracy of SPH method, which shows the relationship between the selected functions and their SPH approximations. The entire involved system was represented by a finite number of particles that carry individual mass and occupy individual space, and the integral interpo- lation was approximated by a summation interpolation. In addition, error comparison was made between SPH method with and without the present improvement.