P2P live streaming systems have been widely adopted nowadays. However, the flash crowd still poses challenges in such P2P systems, which often occurs when an enormous number of users suddenly arrive to view a newly released live program. Facing so many new users, a P2P streaming system usually can not provide reasonable quality of service and these new users often suffer from a long startup delay and a high service rejection rate. In this paper, we propose a bandwidth-aware peer selection method to alleviate the flash crowd. To use the rare available bandwidths more effectively, we let new peers send more requests to the high-bandwidth parents and less requests to the low-bandwidth parents, aiming to make the upload rate of each parent match well with its upload capacity. Moreover, two analytical models are also constructed to evaluate our method and the traditional random peer selection method. Both model analysis and simulation experiment reveal the merits of our method in tackling the flash crowd, in terms of growth of system scale, average startup delay and rejection rate, compared with the random peer selection method.