The continuous finite-time anti-disturbance control problem for a class of nonlinear system under external disturbances and parameter uncertainties is investigated in this article. First, a continuous terminal sliding mode control (CTSMC) is introduced to stabilize the nominal system dynamics. Concerning the unsatisfying performance of the CTSMC in the presence of severe external disturbances and parameter uncertainties, a finite-time disturbance observer (FTDO) is employed to estimate the uncertainties to its nominal dynamics. By integrating the CTSMC method with the FTDO technique, a composite controller is presented for such kind of nonlinear system under external disturbances and parameter uncertainties. The composite controller obtains finite-time convergence property in the presence of disturbances and also nominal control performance recovery in the absence of disturbances. Moreover, compared with conventional sliding mode control, the proposed control law is continuous and no chattering phenomenon exists. The property of stability and the finite-time convergence of the closed-loop system under the proposed controller is guaranteed by means of Lyapunov stability criteria. The proposed control method is finally applied for the tracking control problem of robotic manipulators. Simulation results show that the proposed method exhibits promising control performance in the presence of severe external disturbances and parameter uncertainties.