Trajectory design is one of the key technologies of air-to-air missiles, and proper trajecotry can improve the operational performance of air-to-air missiles significantly. Aiming at the actual operational requirement of air-to-air missiles, the mathematical description of trajecotry design problem is established, in which the missile’s terminal velocity is taken as the performance index and the angle of attack and sideslip angle are taken as the control input. Based on the pseudospectral methods, the states equations and control input of missile are approximated by parameterization and then the dynamic optimization problem is solved by nonlinear programming. Finally, simulation experiments are carried out to verify the validity of the trajectory design medthod. The simulation results show that the inerception trajectory of air-to-air missile can be calculated accurately by the proposed approach and the missile’s terminal velocity is higher than that of proportional guidance, thus the proposed approach can be used for extended range trajectory deisgn of air-to-air missile.