In order to improve the efficiency of beamforming for millimeter-wave communications, a codebook is designed and a corresponding beam search algorithm is proposed in this paper. The codebook is designed with a feature of hierarchy, and can be organized into a binary tree, which makes the implementation of binary search possible. Meanwhile, based on the designed codebook, a suboptimal binary search like (BSL) algorithm is proposed for beamforming. Theoretical analysis and simulation results show that, compared with the state-of-the-art search schemes, the proposed scheme dramatically decreases the search time.