In a P2P (Peer-to-Peer) VoD (video-on-Demand) streaming system, the nodes' load is an important factor which affects the system performance. In the system, some nodes may receive too many requests, which leads to overload. On the other hand, some other nodes may receive too few requests, which leads to low utilization. Therefore, designing a reasonable load balancing strategy is important. However, existing related studies cannot handle this problem effectively, because they don't have an efficient dynamic load information management mechanism, and they don't distinguish the difference of requests when transfer the nodes' load. In this paper, to manage the dynamic load information efficiently, we design a load management table for each node. Based on the load information, we propose a load balancing strategy which uses a request migration algorithm (LBRM). Through simulations, our scheme can handle the load imbalance problem effectively and improve the users' playback fluency.