ABSTRACT Considering the internal, external uncertainties and robustness decreases, this paper addresses an adaptive neural trajectory tracking non-affine control method for a hovercraft under multiple safety constraints. Firstly, hovercraft’s non-affine model has been built and aim to approximate non-affine formulations, a neural network (NN) is utilized. Secondly, to stabilize the position errors, virtual surge velocity control law is obtained via a log-type barrier Lyapunov function (LBLF). Thirdly, a new asymmetric integral barrier Lyapunov function (AIBLF) is presented to address asymmetric safety constraint problems of hovercraft. Aim to guarantee heading control, the yaw angular velocity is obtained consequently. The proposed adaptive method can guarantee the surge velocity and yaw angular velocity to the inside of asymmetric boundaries with the requirements of safe performance during motion. The total system states are ultimately uniformly bounded (UUB) via Lyapunov stability theories. Finally, obtained simulations results demonstrate the effectiveness of the proposed control scheme.