The marine lifting arm system is a novel type of lifting equipment for the dismantling of large offshore platforms. In practical application, the marine lifting arm system is commonly subject to unexpected disturbances such as persistent vessel-induced disturbances, uncertain dynamics, and physical constraints, posing significant challenges for controller system design. This paper proposes a neural network (NN) based adaptive tracking control method with state constraints for the marine lifting arm system to effectively compensate for vessel motions induced by wave disturbances. First, the dynamic model of a marine lifting system is established by employing Lagrange’s method. Subsequently, a nonlinear controller is developed based on the dynamic model to compensate for 3-DOF vessel motions, including heave, roll, and pitch motion. By constructing constrained terms, the nonlinear controller effectively restricts the lifting arm’s motion within the predefined range, ensuring the safety of lifting operations even under adverse sea conditions. The neural network is employed to estimate parameter/structure uncertainties and the nonlinear input dead zones for lifting arm systems. In particular, the designed update law of the neural network considers physical constraints, thereby further ensuring that the lifting arm operates within the safe range. The theoretical stability of the proposed control system is rigorously proven using the Lyapunov technique. Finally, the practicality and effectiveness of the proposed method are verified by the hardware experiments on a self-built offshore lifting system.