In this paper, an adaptive backstepping control scheme is proposed to solve the the surge motion tracking control problem of an autonomous undersea vehicle (AUV) with system constraint. First, an initial rectification reference signal is constructed for the subsequent implementation of deferred output constraint and making the control input smaller and smoother in the early stage of system operation. Second, a barrier Lyapunov function is adopted for developing an output-constrained state feedback adaptive controller. Then, on the basis of coordinate transformation and estimating the derivative of surge displacement by a linear and nonlinear combined differentiator, we develop an output feedback adaptive backstepping control scheme for AUVs whose velocity signals are unmeasurable. We also carried out a comparative numerical simulation with traditional adaptive control to verify the feasibility of the proposed control strategy.