This paper proposes a novel relay selection strategy based on the feedback beamforming (BF) information for 60GHz millimeter-wave (mmWave) wireless communication systems under non-line-of-sight (NLoS) condition. First, an approach of collecting instantaneous channel state information (CSI) through overheard during BF is devised. Second, with the aim of maximizing overall network throughput capacity, the optimal relay selection issue for NLoS links is formulated as a bipartite graph, and the Kuhn Munkres (KM) algorithm is provided to resolve it. Third, both theoretical analysis and simulation results show that the improvements achieved over the best harmonic mean selection scheme in terms of overall network throughput capacity and outage probability.