This article focuses on the time-minimum path planning problem of autonomous underwater vehicles (AUVs) with the constraint of simultaneous arrival in an ocean environment. The overall framework can be divided into two successive modules, and both of them are solved by the biased min-consensus (BMC) method, which introduces the edge weight into the standard min-consensus protocol. The first module plans each AUV's path under the BMC protocol, respectively, along which the AUV will avoid obstacles and navigate to the destination with the minimum time through the ocean current. Incorporating the cooperative constraint of simultaneous arrival, the second part chooses the AUV path with the maximal voyage time as a benchmark, and replans other AUVs’ paths using the BMC method until their corresponding voyage time is approximately equal to the benchmark. The simulation results in various scenarios demonstrate the strong applicability and high effectiveness of our method.