In this paper, we discuss stabilization problem for a class of second-order nonlinear systems with output constraints. At first, as a constraint-handling tool, we design a new barrier Lyapunov function, which has patch-like characteristic and can save control power effectively. Then, the stabilization problem for the system is discussed by applying adding a power integrator and our new barrier Lyapunov function together. Finally, simulations are performed to demonstrate the effectiveness of the proposed results.