A singularity‐free terminal sliding mode (TSM) control scheme with fast and fixed‐time convergence for a class of second‐order non‐linear systems with matched uncertainties and external disturbances is proposed. A novel singularity‐free fast TSM (SFTSM) structure is constructed and the upper‐bound of convergence time is independent of initial states and can be set arbitrarily in advance. Then, the proposed SFTSM controller is designed by combining the SFTSM structure and the composite fast reaching law and the globally fixed‐time stability is guaranteed and derived with the phase plane analysis and Lyapunov stability theory. Finally, the simulation results for a single inverted pendulum tracking system are included to verify the effectiveness of the proposed control method.