In this paper, a real-time quasi-optimal trajectory planning scheme is employed to guide an autonomous underwater vehicle (AUV) safely into a funnel-shape stationary docking station. By taking advantage of the direct method of calculus of variation and inverse dynamics optimization, the proposed trajectory planner provides a computationally efficient framework for autonomous underwater docking in a 3D cluttered undersea environment. Vehicular constraints, such as constraints on AUV states and actuators; boundary conditions, including initial and final vehicle poses; and environmental constraints, for instance no-fly zones and current disturbances, are all modelled and considered in the problem formulation. The performance of the proposed planner algorithm is analyzed through simulation studies. To show the reliability and robustness of the method in dealing with uncertainty, Monte Carlo runs and statistical analysis are carried out. The results of the simulations indicate that the proposed planner is well suited for real-time implementation in a dynamic and uncertain environment.