The coverage path planning (CPP) technique attracts growing interest in studies on underwater search and rescue (SAR) conducted with an autonomous underwater vehicle (AUV) equipped with a side‐scan sonar (SSS). In SAR missions, prior information is crucial. Aiming at the underwater SAR mission with prior information, a new coverage path planner (SAR‐A*) is proposed. The ultimate goal is to generate a feasible path for completely covering the task area and preferentially visiting more valuable cells with fewer turns. First, the whole task area is decomposed into hexagon cells as waypoints to be visited for complete coverage. Second, the probability of discovering the target is obtained according to the target presence probability and the SSS detection ability. Under the assumption of prior target information, the target presence probability is modelled as a two‐dimension Gaussian distribution based on predicted target locations or trajectories. Then, an optimal next‐waypoint selection process is formulated as a multi‐objective decision‐making problem and solved by the weighted metric method. Finally, simulation and experimental results demonstrate that the generated path can improve the cumulative probability of discovering the target with fewer turns.