This article proposes a fixed-time singularity-free neural control scheme for hypersonic flight vehicle (HFV) considering asymmetric time-varying angle of attack (AOA) constraint based on integral barrier Lyapunov function (IBLF). In contrast to the state-of-the-art fixed-time control methods for HFV with AOA constraint, the most distinguishing feature of our control design lies in designing a direct AOA-constrained control scheme without needing error transformation and the singularity issue is avoided. The IBLF is adopted to confine the AOA within a predefined asymmetric time-varying compact set all the time. Moreover, the tracking errors of flight states and the estimate errors of approximations are ensured to converge into the bounded compact sets within fixed time, which can be preset by selecting the design parameters properly. Comparative simulations verify the superiority of the developed methodology.