Forces and dynamic equations of supercavitating vehicles were analyzed in detail in the paper; the mathematic model of the optimal diving trajectory was established in the vertical plane. Considering the time-delay effect during the expansion and contraction of supercavity, the Time Delay Gauss Pseudospectral Method(TDGPM) was introduced. Based on the information of discretized nodes, the TDGPM interpolated the real time cavity shape for each node and calculated the dynamic equations, which were used as constraints during the optimization process. Numerical solution of optimal diving trajectories and corresponding maneuvers were obtained. Results show that supercavitating vehicles without fins can achieve stable and maneuverable flight by applying proper cavitator control. Results also indicate the feasibility of TDGPM and its fast convergence.