Addressing the domain shift challenge between datasets is critical to maintaining model performance. However, existing methods rarely consider the behavior of the human brain when dealing with the domain shift, resulting in poor model segmentation results. Brain-inspired strategies can enhance the migration ability and generalization performance of deep learning models across different data sets by simulating the mechanisms of the human brain in processing complex visual information. Inspired by this, we propose a Brain-inspired Domain Adaptation Network (BDANet) to solve the domain shift problem. Specifically, we adopt the teacher-student architecture for mutual learning and adversarial learning. Both the teacher and student models contain a dual-branch encoder and a brain-inspired decoder for object segmentation. Inspired by the cognitive process of the human brain, we propose a brain-inspired fusion module in the dual-branch encoder to effectively fuse the dual-branch features to obtain complete object information. In the brain-inspired decoder, we propose a brain-inspired refinement module to gradually refine the initial segmentation result and accurately segment the edges of objects. Extensive experiments demonstrate that the proposed method significantly outperforms the existing competitors on the challenging benchmark dataset under evaluation metrics.