Steady glide trajectory optimization for high lift-to-drag ratio reentry vehicle is a challenge because of weakly damped trajectory oscillation. This paper aims at providing a steady glide trajectory using numerical optimal method. A new steady glide dynamic modeling is formulated via extending a trajectory-oscillation suppressing scheme into the three-dimensional reentry dynamics with a spherical and rotating Earth. This scheme comprehensively considers all factors acting on the flight path angle and suppresses the trajectory oscillation by regulating the vertical acceleration in negative feedback form and keeping the lateral acceleration invariant. Then, a study on steady glide trajectory optimization is carried out based on this modeling and pseudospectral method. Two examples with and without bank reversal are taken to evaluate the performance and applicability of the new method. A comparison with the traditional method is also provided to demonstrate its superior performance. Finally, the feasibility of the pseudospectral solution is verified by comparing the optimal trajectory with integral trajectory. The results show that this method not only is capable of addressing the case which the traditional method cannot solve but also significantly improves the computational efficiency. More importantly, it provides more stable and safe optimal steady glide trajectory with high precision.