Path planning is a critical component of robotic navigation. Although existing path planning methods have been widely successful, they often fall short in dynamic pursuit scenarios. In these scenarios, the path must enable a robot to start from an initial state, navigate around obstacles, and ultimately intercept a moving target. In this work, we introduce the dynamic A* algorithm, designed specifically for dynamic pursuit. This algorithm integrates the kinodynamic information of both the robot and the target, incorporating travel time into the calculation. As new nodes are expanded from the current node, the updated position of the target is estimated based on the corresponding travel time, and the heuristic map is refreshed to reflect the latest target position. This enables dynamic interception predictions for moving targets. To further enhance search efficiency, an optimal boundary value problem is solved for analytical expansion. Our simulation experiments demonstrate that the algorithm excels in dynamic pursuit scenarios within plane environments, adhering to motion constraints and adapting to moving targets. Additionally, the algorithm balances time and energy consumption while effectively managing dynamic obstacles, making it a powerful tool for addressing similar challenges.