In this paper, adaptive control is presented for a class of parametric output feedback nonlinear systems with output constraint. Adaptive observer backstepping is adopted to achieve the output tracking. To prevent the output constraint violation, the Barrier Lyapunov Function (BLF) is employed in Lyapunov synthesis. By ensuring the boundedness of the BLF, we also guarantee that the output constraint is not transgressed. Compared with the control using a Quadratic Lyapunov Function (QLF), our control requires less restrictive initial conditions. The stability analysis of the closed-loop system is provided and all closed-loop signals are ensured to be bounded. Simulation results demonstrate the effectiveness of the proposed approach.