In order to solve the fast calculation of the free trajectory considering the effects of the earth non-spherical gravitation, the differential equations of motion under the earth gravitation including the J₂-perturbation were established in the non-orthogonal coordinate system, and the differential equations of motion under disturbing gravity were established in the orbital coordinate system. The acceleration of upward disturbing gravity was equivalent to the mass deviation of the earth, and introduced into the standard elliptical orbit. The differential equations under J₂-perturbation were modified, and the parameters of the position and velocity were calculated under the analytical solution. The simulation results show that the analytic solution has a higher efficiency, and the position error of impact point is within 20 meters. The analytic solution satisfies the requirement of the real-time guidance and orbit forecast.