In this paper, we consider a wireless-powered cooperative communication network, which consists of one hybrid access point (AP), one source and one relay to assist information transmission. Unlike conventional cooperative networks, the source and relay are assumed to have no embedded energy supplies in the considered system. Hence, they need to first harvest energy from the radio-frequency (RF) signals radiated by the AP in the downlink (DL) before information transmission in the uplink (UL). Inspired by the recently proposed harvest-then-transmit (HTT) and harvest-then-cooperate (HTC) protocols, we develop a new adaptive transmission (AT) protocol. In the proposed protocol, at the beginning of each transmission block, the AP charges the source. AP and source then perform channel estimation to acquire the channel state information (CSI) between them. Based on the CSI estimate, the AP adaptively chooses the source to perform UL information transmission either directly or cooperatively with the relay. We derive an approximate closed-form expression for the average throughput of the proposed AT protocol over Nakagami-m fading channels. The analysis is then verified by Monte Carlo simulations. Results show that the proposed AT protocol considerably outperforms both the HTT and HTC protocols.