To improve the efficiency of multiple Autonomous Underwater Vehicles (multi-AUV) cooperative target search in a Three-Dimensional (3D) underwater workspace, an integrated algorithm is proposed by combining a Self-Organising Map (SOM), neural network and Glasius Bioinspired Neural Network (GBNN). With this integrated algorithm, the 3D underwater workspace is first divided into subspaces dependent on the abilities of the AUV team members. After that, tasks are allocated to each subspace for an AUV by SOM. Finally, AUVs move to the assigned subspace in the shortest way and start their search task by GBNN. This integrated algorithm, by avoiding overlapping search paths and raising the coverage rate, can reduce energy consumption of the whole multi-AUV system. The simulation results show that the proposed algorithm is capable of guiding multi-AUV to achieve a multiple target search task with higher efficiency and adaptability compared with a more traditional bioinspired neural network algorithm.