In the present paper, the observer-based composite adaptive terminal sliding-mode control is investigated for the nonlinear uncertain system. First, an adaptive observer is designed to estimate the unavailable high-order derivative of the output. Then, a new dynamic terminal sliding surface is proposed with a state filter, which aims to develop the dynamic terminal sliding mode controller. By the composite adaptive control methods, a new adaptive law is designed, and the stability of the overall system is proofed based on the Lyapunov method. Finally, some numerical simulations are conducted to validate the effectiveness of the proposed algorithm.