A novel composite terminal guidance law with impact angle constraints is proposed for supercavitating torpedoes to intercept maneuvering warships. Based on an adaptive super-twisting algorithm and nonsingular terminal sliding mode (NTSM), the proposed guidance law can guarantee the finite-time convergence of line-of-sight (LOS) angle error and the LOS angular rate error. The new guidance law is a combination of finite-time stability theory, sliding mode control (SMC), tracking differentiator (TD), disturbance observer (DO), and dynamic surface control. A high-order sliding mode TD is used for denoising, tracking, and differentiating the measured target heading angle. A novel DO, with its finite-time stability proved, is designed to estimate the target lateral acceleration for feedforward compensation to attenuate chattering in control input. In the case of a first-order-lag autopilot, a new kind of tracking differentiator is adopted to compute the first-order time derivative of the virtual control command, which can improve the accuracy of dynamic surface control and avoid the “explosion of items” problem encountered with the backstepping control. Finally, numerical simulation results are presented to validate the effectiveness and superiority of the proposed TD, DO, and the composite guidance law.