In response to the increasing need for stable power supply and reliable communication services in remote regions worldwide, Low Earth Orbit (LEO) satellites offer a promising solution owing to the difficulty of deploying traditional power communication infrastructure in remote areas and their vulnerability to natural disasters. Considering the demand of high mobility of LEO satellites that require frequent handover to maintain service continuity, one of the main technical challenges for LEO satellite networks is how to manage satellite handover to ensure the continuity of communication services. Therefore, it becomes crucial to study optimization techniques for satellite handover, and We introduce an optimization approach for handover that integrates Graph Neural Networks (GNN) with Deep Reinforcement Learning (DRL). The simulation results show that our proposed handover method (MPNN-DQN) outperforms the DRL-based approach in reducing handover frequency and communication delay.