In order to solve the problem of chattering and slow global convergence of the traditional power law, a new compound sliding mode law is proposed, which introduces a tangent function and improves the traditional power law, thus the fast convergence and chattering-free characteristics of the reaching law are realized. Firstly, a tangent function is introduced, which can make the system converge faster when the initial state is known, the reaching law is designed to improve the chattering caused by the product term of the symbolic function in the traditional power reaching law. Then, the convergence rate and steady-state error bounds of the new compound reaching law are derived. Finally, taking the magnetic levitation system of a linear magnetic levitation synchronous motor as an example, the simulation results show that the new compound reaching law can obviously shorten the dynamic process of the system and eliminate chattering, and in the presence of model uncertainty and external disturbance, the system can converge rapidly to the region near the equilibrium point.