Considerable advances have taken place in the area of sensor technology, which have lead smaller, less expensive sensing devices with higher processing, sensing, storage, and communication capabilities. Consequently, many environmental, commercial, and military applications have emerged for wireless sensor networks (WSNs). Such WSNs can be used in the important field of oil, gas, and water pipeline monitoring. In this type of WSNs, due to the nature of the monitored structure, the nodes are lined up in a linear form, making a special class of these networks; We defined these in a previous paper as Linear Sensor Networks (LSNs). This paper focuses on using LSNs to monitor underwater pipelines where data is collected from the sensor nodes (SNs) and transmitted to a surface sink using an autonomous underwater vehicle (AUV). In turn, the surface sink can transmit the data to the network control center (NCC) using the communication infrastructure that is available in the corresponding region (e.g. WiMAX, cellular, GPRS, satellite communication, etc.) We name this network architecture an AUV-based LSNs (ALSNs). The use of the AUV is due to the fact that a pure multihop approach to route the data all the way along the linear network which can extend for hundreds or even thousands of kilometers can be very costly from an energy dissipation point of view, thereby reducing the effective lifetime of the network. With this approach a significantly smaller transmission range can be used by the SNs. Furthermore, the strategy provides for reduced interference between the SN transmissions that can be caused by hidden terminal and collision problems, that would be expected if a pure multihop approach is used. Finally, different AUV movement strategies are offered and analysed under various network conditions with respect to the performance of important system metrics such as average data packet end-to-end delay and delivery ratio.