The Runge-Kutta-Fehlberg algorithm(RKF),the symplectic algorithm and the Hermite algorithm for N-body problems are studied with energies errors and semimajor axis and eccentricity.It shows that the precision of RKF is the highest,but its error increases with computation time.The symplectic algorithm has no artificial dissipation,and keeps stability of the energy error.The structure of the Hermite algorithm is simple and its computation time is short,but its error is greater than that of the other two.