This paper presents a robust entry guidance algorithm for the high lift-to-drag ratio entry vehicle that employs the recently developed pseudospectral model predict control in a segmented manner. Here, the guidance commands are the longitudinal liftto-drag(L/D) and bank reversal commands, which are calculated by successively solving multiple segment linear algebraic equations. These equations are derived using the linear pseudospectral method, control parametrization and calculus of variations. The method uses orthogonal polynomials and computes the updates through a series of analytical formulae, which makes it accurate and computationally effective. Moreover, it is able to adjust the number of bank reversals by providing the precise bank reversal point so as to fully exploit the potential of lateral maneuver.The method also employs proportional navigation and polynomial guidance after the last bank reversal to meet multiple terminal constraints. High-fidelity numerical simulations with various destinations are carried out to demonstrate its applicability. Furthermore, Monte Carlo simulations are also conducted to show that the proposed algorithm consistently offers very stable and robust performances and has superior performances in computational efficiency, guidance accuracy and lateral trajectory shaping capability in comparison with other typical methods. This paper presents a robust entry guidance algorithm for the high lift-to-drag ratio entry that that the recently developed pseudospectral model predict control in a segmented manner. Here, the guidance commands are the longitudinal liftto-drag (L / D) and These equations are derived using the linear pseudospectral method, control parametrization and calculus of variations. The method uses orthogonal polynomials and computes the updates through a series of analytical formulae, which makes it accurate and computationally effective. Moreover, it is able to adjust the number of bank reversals by providing the precise bank reversal point so as to fully exploit the potential of lateral maneuver. The method also includes rule navigation and polynomial guidance after the last bank reversal to meet multiple terminal constraints. High-fidelity numerical simulations wi Further, Monte Carlo simulations are also conducted to show that the proposed algorithm ologies offers very stable and robust performances and has superior performances in computational efficiency, guidance accuracy and lateral trajectory shaping capabilities in comparison with other typical methods.