Brain science and brain-inspired artificial intelligence have the potential for strengthening business and management. Brain-inspired artificial intelligence (AI) uses principles of brain science to build algorithms and AI systems with human-like intelligence. Some concepts (e.g., cognition, inference, memory, and intelligence) and principles of brain science are introduced in this paper. The research progress in several topics are also presented that include brain-inspired artificial intelligence and brain-inspired computing, project management and brain-inspired management, the integration of brain science into leadership (especially crisis leadership), and brain-inspired decision-making for business. Future research and trends in some topics are introduced.