For the challenge of ensuring safety navigation of underactuated hovercraft in the presence of system uncertainties, this paper proposes an innovative adaptive safety trajectory tracking control strategy for hovercraft based on the nonlinear mapping function (NMF). The strategy not only eliminates constraints on boundaries but also can directly dealing with both constrained and unconstrained cases. Additionally, a novel composite anti-disturbance method is proposed, utilizing the neural network (NN) approximator and the nonlinear disturbance observer (NDO). Moreover, a novel first-order filter is designed to address the intricate differential computation issues in the backstepping control. The system's stability is examined using Lyapunov stability theory, showing that tracking errors converge to become ultimately uniformly bounded (UUB). Simulation results affirm the effectiveness and superiority of the proposed adaptive trajectory tracking control strategy.