Due to the merits of lower bandwidth consumption at streaming server and higher scalability, P2P streaming systems are widely adopted and deployed. However, the heterogeneity of bandwidth resource and playback position at peers may easily lead to load unbalancing problem. This may severely deteriorate video playback quality at peers. This paper focuses on the issue of bandwidth request allocation, aiming at substantially balancing the load at the peers in P2P streaming network. The problem of contending service from multiple neighboring peers is modeled as a non-cooperative game, and the optimal bandwidth request allocation policy, called Game based Bandwidth Request Allocation (GBRA), is obtained through searching the Nash equilibrium of this game. Numerical results show that the proposed policy can effectively improve the load balancing of the P2P streaming networks and decrease the latency of streaming data retrieval at peers when compared with the classical bandwidth request allocation policies.