To weaken the nonlinear coupling influences among the variables in the speed and tension system of reversible cold strip rolling mill, a novel dynamic decoupling control strategy is proposed based on nonsingular fast terminal sliding mode (NFTSM) and wavelet neural network (WNN). First, nonlinear disturbance observers are developed to counteract the mismatched uncertainties, and then input/output dynamic decoupling and linearisation for the speed and tension nonlinear coupling system are realised by utilising the inverse system theory. Second, nonsingular fast terminal sliding mode controller (NFTSMC) for each pseudo linear subsystem is presented based on backstepping and two-power reaching law, so as to improve the global convergence speed and robust stability of the system. Third, adaptive WNNs are used to approximate the uncertain items of the system, so as to improve the control precision of the speed and tension of reversible cold strip rolling mill. Theoretical analyses show that the NFTSMs satisfy reachability condition, the system error variables can converge to equilibrium point in finite time, and the resulting closed-loop system is globally asymptotically stable. Finally, simulation research is carried out on the speed and tension system of a 1422 mm reversible cold strip rolling mill by using the actual data, and results show the superiority of the proposed control strategy in comparison with the strategies of cascade PI, linear sliding mode control and internal model control.