This paper proposes cooperative routing algorithms to improve the performance of underwater acoustic sensor networks (UW-ASNs). With the consideration of the poor acoustic link quality, a cross-layer design of physical layer and network layer is described for selecting simultaneously routing relays (RR) for forwarding data on routing paths and cooperative relays (CR) for one-hop cooperative communications. In the networks, sources that have data to transmit independently selects their own relays (i.e., both RR and CR) among their neighbors based on their link quality indicators (i.e., signal-to-noise ratio (SNR), time of arrival (ToA)) and their physical distances represented by hop count (HC) to the destination. Exploiting packet receiving or overhearing in the networks, these parameters are averaged and updated frequently to adapt to the unreliable and varying characteristics of acoustic channel over the time. By this way, the “best” relays with the “best” estimated measurements are selected reliably. Our simulation results show that the proposed algorithms improve the network performance in terms of end-to-end delay, energy consumption and packet delivery ratio.