Trajectory optimum design for flight vehicles using pseudo-spectral methods has been a hot research direction in recent years, but studies about the overview of this field are very few. Based on the systematic research of domestic and overseas related literatures, the basic principles of several pseudo-spectral methods which have a wide range of applications in aerospace field were expounded; the thoughts and formulas for transforming continuous optimal control problems into nonlinear programming problems were concluded; the applications of pseudo-spectral method in the trajectory optimum design for flight vehicles were summarized; the development directions of pseudo-spectral method and its application in trajectory optimization design for flight vehicles were discussed.