An adaptive neural network (NN) control is proposed for an unknown two-degree of freedom (2-DOF) helicopter system with unknown backlash-like hysteresis and output constraint in this study. A radial basis function NN is adopted to estimate the unknown dynamics model of the helicopter, adaptive variables are employed to eliminate the effect of unknown backlash-like hysteresis present in the system, and a barrier Lyapunov function is designed to deal with the output constraint. Through the Lyapunov stability analysis, the closed-loop system is proven to be semiglobally and uniformly bounded, and the asymptotic attitude adjustment and tracking of the desired set point and trajectory are achieved. Finally, numerical simulation and experiments on a Quanser's experimental platform verify that the control method is appropriate and effective.