In order to deal with the channel fading in Underwater Wireless Sensor Networks (UWSN) changing randomly in time-space-frequency domain, underwater cooperative communication model with relays was proposed in this paper to improve reliability and obtain diversity gain of the communication system. Based on the new model, a relay selection algorithm for UWSN was proposed. The new relay selection algorithm used new evaluation criteria to select the best relay node by considering two indicators: channel gain and long delay. With the selected relay node, source node and relay nodes could adjust their sending power by the power allocation algorithm which was based on the principle of minimizing the bit error rate. In a typical scenario, by comparing with the traditional relay selecting algorithm and equal power allocation algorithm, the new algorithm reduces the delay by 16.7% and lowers bit error rate by 1.81dB.