In this paper, we focus on the use of linear sensor networks (LSNs) to monitor underwater pipelines. We propose the use of autonomous underwater vehicles (AUVs) to move along pipeline segments and collect data from the sensor nodes (SNs). Each AUV then delivers the collected data to the surface sink at the end of the corresponding LSN segment. In turn, the surface sink transmits the collected data to the network control center using any of the communication technologies that are available in the area such as WiMAX, cellular, and satellite. The use of AUVs for data collection offers considerable advantages including flexibility in SN placement, considerable energy savings and reduced interference, hidden terminal problems, and collisions. We also provide, different AUV movement strategies and analyze the effect of various network design parameters on network performance metrics such as packet delivery ratio and end-to-end delay.