As a kind of fuel cells, solid oxide fuel cell (SOFC) has been an important research area for researchers. However, SOFC gives a challenging control problem because of their operating constraints, complex nonlinearity, slow dynamics, and load disturbance. In this article, a new enhanced model-free discrete-time adaptive terminal sliding-mode control (EMF-ATSMC) is proposed for the SOFC system with input constraints, aiming to regulate the output voltage under the load disturbance. The referred EMF-ATSMC controller is composed of three components: the pseudo-partial-derivative (PPD) estimator, the discrete-time adaptive terminal sliding-mode control, and the anti-windup compensator. First, an enhanced compact form of dynamic linearization data-driven modelling method is used to simplify the SOFC plant considering the load perturbation, and then, the PPD estimator is designed. The discrete-time adaptive terminal sliding-mode control via anti-windup compensator is developed to improve the control performance and guarantee the controlled system stability, wherein the designed anti-windup compensator is employed to eliminate the magnitude and rate saturations of control input. Moreover, the closed-loop system's stability with the proposed EMF-ATSMC controller is theoretically proved by using the Lyapunov method. Finally, simulation results are given to demonstrate that the proposed EMF-ATSMC controller has excellent dynamic performance and stronger robustness compared with other methods such as improved model-free adaptive constrained control (IMFACC), model-free adaptive control (MFAC), and PID controller.