Multi-AUV real-time hunting is a comprehensive research topic, including team collaboration and pursuit of targets. In this paper, the hunting time for an evader is first estimated using a fast marching algorithm, and then a dynamic hunting alliance is formed between AUVs. Then, in the hunting phase, the AUV needs to track the evader immediately to prevent it from escaping. In order to achieve this goal, an additional attenuation term is added in the GBNN(Glasius biological inspired neural network) model, the inverse function instead of exponential function is also applied in calculating the connection weights of neurons, and two improvements to accelerate the propagation of neuronal activity are proposed, which make the GBNN model suitable for real-time path planning. Simulation studies show that the hunting alliance formation mechanism and the improved GBNN model both have their advantages. In the underwater multi-AUV cooperative hunting, the proposed hunting control algorithm improves the hunting efficiency, and reduces the hunting distance of the AUVs and the escaping distance of the evader.