Abstract: The smoothed particle hydrodynamics(SPH) is one of mesh-free methods and has been widely developed during these years.This numerical method has many advantages for free surface problems and large deformation problems,because of its mesh-free andLagrangian characters.But this method still exists some disadvantages at present,like low accuracy of calculation,rmre computational expense.According to the shortcomings of onginal SPH method,this paper focuses on the impnwement of precision.Fnrstly,the foundation theory of onginal SPH method is introduced in brief,according to the precision analysis,the ream of low precision for the traditional method is pointed out,and second order SPH method is introduced.Then though the verification and analysis of accuracy,it is concluded that the precision of this new method achieves second order.Rnally,based on the twa dimension numerical tests,the error distributions of the function values,first order and second order derivatives are given by the original and modified method,when the particles are arranged at two ways,uniform distribution and non-uniform distribution.The results demonstrate that the second order method can overcome some shortcoming of the traditional method,and the precision can be improved effectively.