The output tracking controller design problem is dealt with for the nonlinear semi-strict feedback systems in the presence of mismatched nonlinear uncertainties. The controller is designed in a backstepping manner, and to avoid the shortcoming of "explosion of terms", the dynamic surface control technique is adopted. At each step of the virtual controller design, a robust feedback controller employing some effective nonlinear damping terms is designed to guarantee input-to-state practical stable property of the corresponding subsystem, so that the system states remain in the feasible domain. The virtual controller is enhanced by a finite-time disturbance observer which estimates the disturbance term in a finite-time. The properties of the composite control system are analyzed theoretically.