Pursuing a moving target in modern computer games presents several challenges to situated agents, including real-time response, large-scale search space, severely limited computation resources, incomplete environmental knowledge, adversarial escaping strategy, and outsmarting the opponent. In this paper, we propose a novel tracking automatic optimization moving-target pursuit (TAO-MTP) algorithm employing improved tracking strategy to effectively address all challenges above for the problem involving single hunter and single prey. TAO-MTP uses a queue to store prey's trajectory, and simultaneously runs real-time adaptive A* (RTAA*) repeatedly to approach the optimal position updated periodically in the trajectory within limited steps, which makes the overall pursuit cost smallest. In the process, the hunter speculatively moves to any position explored in the trajectory, not necessarily the optimal position, to speed up convergence, and then directly moves along the trajectory to pursue the prey. Moreover, automatic optimization methods, such as reducing trajectory storage and optimizing pursuit path, are used to further enhance its performance. As long as the hunter's moving speed is faster than that of the prey, and its sense scope is large enough, it will eventually capture the prey. Experiments using commercial game maps show that TAO-MTP is independent of adversarial escaping strategy, and outperforms all the classic and state-of-the-art moving-target pursuit algorithms such as extended moving-target search (eMTS), path refinement moving-target search (PR MTS), moving-target adaptive A* (MTAA*), and generalized adaptive A* (GAA*).