Abstract: A new entry guidance law for the high lift to drag ratio gliding vehicle was proposed on the basis of the linear pseudospectral model predictive control method. Adopting this approach, the vehicle can arrive at the end of the entry flight with the specific heading angle. Moreover, all the typical constraints such as terminal state constraints and path constraints can be satisfied as well. Firstly, the agent technology using high dimensional polynomials was applied to generalize the lift to drag ratio, hence the analytical expression of the lift to drag ratio was obtained with respect to the energy and the angle of attack. Therefore the angle of attack was designed online to adjust the lift to drag ratio, which can enhance the trajectory planning capacity. The whole entry flight was divided into two phases noted as the descent phase and the gliding phase respectively. In the descent phase, in order to limit the maximum heating rate, the angle of attack remains the maximum allowance value and the bank angle was set to zero. During the gliding phase, the linear pseudospectral model predictive control method was applied. The reduced order dynamic model was formulated to predict the terminal state deviation, and the reduced order dynamic equation was linearized to obtain the error propagation equation. Due to the complexity of the integral calculation, Gauss pseudospectral method was used to derive the correction of the control variables. Finally, terminal state deviations involving final position and heading angle can be efficiently eliminated by modifying the angle of attack parameters, the bank angle parameters and the energy parameters of two bank reversal points. This method is simple and easy to implement with high accuracy, and it is convenient for on-line calculation. The simulation results also show that the planning requirements can be satisfied well through this method.