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In this paper, we propose a buffer-aided relaying protocol for a multiuser relay network consisting of N sources, a relay with a buffer, and a destination. All nodes are equipped with a single antenna and operated in a decode-and-forward half-duplex mode. We assume the direct source-destination links do not exist. Different from the conventional multiuser relaying that the half-duplex relay always alternates between reception and transmission in successive time slots, the proposed protocol enables the relay to choose link to transmit based on the channel state information (CSI). The optimal link selection is derived from throughput maximization under the buffer stability constraint. We solve this optimization problem by relaxing the discrete constraints and applying the Karush-Kuhn-Tucker (KKT) conditions. The threshold of the link selection strategy is obtained under Rayleigh fading channel conditions. The numerical results show that the buffer-aided multiuser relay network with the optimal link selection strategy achieves significant throughput gains compared with conventional multiuser relaying that use the best user selection scheme (BUS) with fixed transmission schedule.