When a vehicle moves underwater, disturbance is generated and a wake remains that destroys the original free surface and produces a new wake. In order to study the mechanism and characteristics of the wave-making wake generated by the maneuvering motion of an underwater vehicle in density-stratified fluid, the k-ε model and the VOF method that is based on the RANS equation were used in this paper to analyze the SUBOFF model in stratified fluid at different drift angles. Numerical simulation of the maneuvering motion was carried out under these angles, and the corresponding changes in flow field caused by this motion were analyzed. The results from the comparison and analysis of the surface wave wakes under different drift angles in stratified fluid show that with the increasing drift angle, the motion wake of the vehicle still exhibits obvious Kelvin wave system characteristics. However, there are significant changes in hydrodynamic performance. The asymmetry of the surrounding flow field will increase with the increase in the drift angle. The pressure of the underwater vehicle is inversely proportional to the velocity of the surrounding flow field, and the amplitude of the peak and trough of the free surface wave is linearly related to the change in the drift angle. The numerical simulation can serve as a reference for the non-acoustic detection of the motion heading of an underwater vehicle and the motion trajectory of anti-reconnaissance underwater vehicles under actual sea conditions.