Path planners in which a hunter is required to chase after a moving target is an important problem for modern robotic systems such as Unmanned Aerial Vehicles (UAVs) and Unmanned Underwater Vehicles (UUVs). This thesis describes an incremental moving target path planning algorithm which leverages previous planning data to update the path in the case where the target moves. The algorithm in this thesis addresses the need for a quick path-planner that can be used in an environment where the target is moving. The algorithm does this by sacrificing optimality in order to reduce the complexity of the problem. The algorithm will be shown to reduce the complexity of re-planning by approximately 12 times while only increasing path length taken by 1.5%. Within this thesis analytical estimates of the best and worst case complexity of the algorithm were developed, and these estimates were validated with experimental data.