Remotely operated vehicles (ROVs) have been popularly applied in a range of complex underwater tasks. To minimize the human operator’s workload and errors, deep reinforcement learning has been introduced to realize autonomous control of ROVs. However, current research on ROV control via deep reinforcement learning mostly focuses on single task learning. In this paper, we proposed and implemented progressive neural networks (PNNs) for ROV multi-task learning. In addition, to improve the robot’s learning efficiency, we further proposed a three-column PNN (SPNN) that dynamically selects the transferring experience from previous path following and obstacle avoidance tasks based on the detected situation in the new path following with local path planning task. We evaluated our methods on Gazebo with the BlueROV2 simulator in two types of tasks: straight line path following with local path planning, sinusoidal curve path following with local path planning. Our results show that ROV trained via PNNs and SPNN can learn to complete path following with local path planning tasks faster than directly transferring policy across multi-tasks (SAC-Multi) and directly trained policy in a single task (SAC-Single) via deep reinforcement learning SAC method, and generalize better to new tasks than the SAC-Multi, SAC-Single and the traditional PID controller.