For multi-Autonomous Underwater Vehicle (multi-AUV) system task assignment and path planning, a novel Glasius Bio-inspired Self-Organising Map (GBSOM) neural networks algorithm is proposed to solve relevant problems in a Three-Dimensional (3D) grid map. Firstly, a 3D Glasius Bio-inspired Neural Network (GBNN) model is established to represent the 3D underwater working environment. Using this model, the strength of neural activity is calculated at each node within the GBNN. Secondly, a Self-Organising Map (SOM) neural network is used to assign the targets to a set of AUVs and determine the order of the AUVs to access the target point. Finally, according to the magnitude of the neuron activity in the GBNN, the next AUV target point can be autonomously planned when the task assignment is completed. By repeating the above three steps, access to all target points is completed. Simulation and comparison studies are presented to demonstrate that the proposed algorithm can overcome the speed jump problem of SOM algorithms and path planning in the 3D underwater environments with static or dynamic obstacles.