Aiming at the problem of large fluctuation of winding tension when the winding system is working, an inverse nonsingular fast terminal sliding mode tension control method based on neural network interval observer is proposed. The mathematical model of the winding system is constructed, and the neural network is used to approximate the random response caused by the change of parameters such as the radius and inertia of the winding system. The interval state observer is designed to estimate the upper and lower bounds of the system speed and the winding tension. According to the estimated state value, the backstepping nonsingular terminal sliding mode controller is constructed to make the tension tracking error converge to zero quickly in a finite time, which effectively enhances the robust performance of the system. The simulation results show that the designed control method makes the tension on the coil reach a given value and remain constant after 1.6 s. Compared with the conventional sliding mode controller and the sliding mode controller in the published literature, the adjustment time is reduced by 57% and 33% respectively, which proves the effectiveness and reliability of the proposed control method and meets the requirements of the winding process of the winding equipment.