Devising intelligent robots or agents that interact with humans is a major challenge for artificial intelligence. In such contexts, agents must constantly adapt their decisions according to human activities and modify their goal. In this extended abstract, we present a novel continual planning approach, called Moving Goal Planning (MGP) to adapt plans to goal evolutions. This approach draws inspiration from Moving Target Search (MTS) algorithms. In order to limit the number of search iterations and to improve its efficiency, MGP delays as much as possible the start of new searches when the goal changes over time. To this purpose, MGP uses two strategies: Open Check (OC) that checks if the new goal is still in the current search tree and Plan Follow (PF) that estimates whether executing actions of the current plan brings MGP closer to the new goal.