How an autonomous underwater vehicle (AUV) performs fully automated task allocation and achieves satisfactory mission planning effects during the search for potential threats deployed in an underwater space is the focus of the paper. First, the task assignment problem is defined as a traveling salesman problem (TSP) with specific and distinct starting and ending points. Two competitive and non-commensurable optimization goals, the total sailing distance and the turning angle generated by an AUV to completely traverse threat points in the planned order, are taken into account. The maneuverability limitations of an AUV, namely, minimum radius of a turn and speed, are also introduced as constraints. Then, an improved ant colony optimization (ACO) algorithm based on fuzzy logic and a dynamic pheromone volatilization rule is developed to solve the TSP. With the help of the fuzzy set, the ants that have moved along better paths are screened and the pheromone update is performed only on preferred paths so as to enhance pathfinding guidance in the early stage of the ACO algorithm. By using the dynamic pheromone volatilization rule, more volatile pheromones on preferred paths are produced as the number of iterations of the ACO algorithm increases, thus providing an effective way for the algorithm to escape from a local minimum in the later stage. Finally, comparative simulations are presented to illustrate the effectiveness and advantages of the proposed algorithm and the influence of critical parameters is also analyzed and demonstrated.