Multi-cell cooperation is a promising technique to mitigate inter-cell interference arising from universal frequency reuse in cellular networks. Sharing channel state information (CSI) in neighboring cells can help enhance the overall system capacity at the cost of high feedback burden. In this paper, an asymmetric CSI feedback strategy is proposed for multi-cell cooperation beamforming. In order to improve the overall system performance, we optimize the limited feedback bandwidth based on the average received power from both serving and neighboring cells. Simulation results show that the proposed strategy utilizes the limited feedback bandwidth more efficiently, thereby achieving a higher sum rate.