Trajectory optimization is a key technology of hypersonic glide vehicle. In order to avoid the disadvantage of indirect method's sensitivity to initial guess and pseudospectral method's difficulty to settle path constraints, a direct method based on Akima spline interpolation is proposed to solve reentry trajectory optimization problem. A numerical example that minimizes the stagnation point heat flux and fly time to target while satisfying state constraints such as vehicle dynamics, control limitation, waypoint, no-fly zone, dynamic pressure and overload is presented. Compared with literature results, the results show that the Akima interpolation can decrease the control parameter's bound violation phenomena during interpolation; the Pareto front distributed nicely, providing more choice to designer during concept design stage. Compared with the single object optimize result in literature, the algorithm adopted in this paper also shows better performance.