A three-dimensional guidance law for maneuvering targets based on super-twisting sliding mode control is proposed. Firstly, a novel multi-variable super-twisting sliding mode algorithm is proposed, and its finite-time stability is proved based on the Lyapunov stability theory. The quantitative analysis of the convergence time is also carried out. Secondly, the missile-target relative kinematics in a three-dimensional engagement scenario is established, and the guidance law design is transformed into a control problem of second-order multi-variable system. Thirdly, a three- dimensional guidance law with terminal angle constraint is designed based on the improved multi-variable super-twisting sliding mode algorithm. Finally, the effectiveness of the proposed method is verified through comparative simulations and Monte Carlo simulation.