This paper proposes a new method for the tracking control problem of strict-feedback systems with mismatched disturbances. The method, called the uncertainty disturbance estimator (UDE), is introduced into the conventional backstepping scheme to handle the mismatched disturbances due to its excellent performance in handling uncertainties and disturbances yet a simple control scheme. The dynamic surface control (DSC) is adopted to overcome the explosion of complexity problem in the backstepping scheme. Compared to the existing work in the literature, the backstepping deviation term between the synthetic virtual control and system state, is lumped into the disturbance-like term, together with the DSC filtering error and mismatched disturbances. The lumped term is then handled by the UDE method at each step, which simplifies the control design and analysis. In addition, the marriage of UDE with backstepping also relaxes the structural constraint of the UDE design for mismatched uncertainties. The uniformly ultimate boundedness of the closed-loop system is proved. Both numerical simulation and experimental validation are carried out to demonstrate the effectiveness of the proposed approach.