This paper presents an algorithm for docking a torpedo-shaped autonomous underwater vehicle (AUV). We propose a new docking assessment algorithm comprising three phases: depth tracking, docking-feasibility region analysis, and docking-success probability evaluation. For depth-tracking analysis, a neural network-generated path is used to satisfy constrained docking conditions of depth and distance. With regard to docking feasibility region analysis, the working space of the AUV can provide a possibility region of successful docking. In the analysis, working space is expressed by a turning ellipsoid, which is the numerical solution of the maximum yawing motion. An algorithm is presented to evaluate the probability of docking success, based on the probability of sensor data. A good contribution of this approach is that a criterion for assessing the feasibility of the desired path for docking is given through the proposed docking assessment algorithm.