An adaptive neural control scheme without backstepping is proposed for the air-breathing hypersonic vehicle subject to input constraints. To estimate the unknown nonlinearity of velocity subsystem and altitude subsystem, two radial basis function neural networks (RBFNNs) are constructed. Since the complex backstepping design steps are not needed, the proposed control structure is quite concise and the problem of "explosion of terms" is avoided. Moreover, a novel nonlinear auxiliary system is constructed to solve the problem of input constraints. The advantage of the proposed auxiliary system is that its high-order form has good performance and the parameter tuning is relatively easy. Simulation results show that the designed controllers achieve stable tracking of reference commands with good performance.