Target search for moving and invisible objects has always been considered a challenge, as the floating objects drift with the flows. This study focuses on target search by multiple autonomous underwater vehicles (AUV) and investigates a multi-agent target search method (MATSMI) for moving and invisible objects. In the MATSMI algorithm, based on the multi-agent deep deterministic policy gradient (MADDPG) method, we add spatial and temporal information to the reinforcement learning state and set up specialized rewards in conjunction with a maritime target search scenario. Additionally, we construct a simulation environment to simulate a multi-AUV search for the floating object. The simulation results show that the MATSMI method has about 20% higher search success rate and about 70 steps shorter search time than the traditional search method. In addition, the MATSMI method converges faster than the MADDPG method. This paper provides a novel and effective method for solving the maritime target search problem.