For an air-breathing hypersonic vehicle (AHV), the high angle of attack (AOA) caused by longitudinal maneuver may lead to the inlet unstart of a scramjet. Therefore, it is necessary to consider the AOA constraint in the controller design of the AHV. In this article, a finite-time neural optimal controller is proposed to satisfy the tracking performance and the AOA constraint simultaneously. First, a basic tracking controller is built to ensure the finite-time convergence of tracking error. Then, a control-oriented safety quantization is investigated. A specific barrier function based on the safety margin is constructed to quantify the safety risk of the AOA. To enforce the AOA constraint in a minimally invasive fashion, a safe adaptive dynamic programming (ADP) is proposed to optimize the basic controller automatically. The specific barrier function is treated as an extended state and, thus, incorporated into the value function of ADP as a risk penalty term for the tradeoff between the tracking performance and the AOA safety constraint. Finally, a safety-considered policy iteration and a single-critic neural network are developed to build an adaptive AOA safety modified policy online. The comparison simulation results show the effectiveness of the proposed controller.