This paper proposes a new trajectory optimization method using lossless convexity to address the multi-constrained trajectory optimization problem of hypersonic gliding vehicle, considering the nonlinear time-varying characteristics of aerodynamic parameters. Firstly, the dynamics and constraint models of the vehicle are established, and the trajectory optimization problem is described. Then, a sequential convex optimization method using lossless convex processing is proposed. In order to describe the nonlinear time-varying drag coefficient accurately, a new convexity method is used in the process of optimization. New variables are defined, and the nonlinear terms in the vehicle dynamics are processed by convexification method. On this basis, the sequential convex optimization architecture has been used to address the optimization problem. Finally, combined with the mission scenario of hypersonic gliding vehicle, the trajectory optimization method based on lossless convexity processing is simulated. The result shows that lossless convexity method could get more reasonable flight path than the linearization method, and has higher solving efficiency.