Acceleration of urbanisation is posing great challenges to sustainable development. Growing accessibility to big data and artificial intelligence (AI) technologies have revolutionised many fields and offered great potential for addressing pressing urban problems. However, using these technologies without explicitly considering responsibilities would bring new societal and environmental issues. To maximise the benefits of big data and AI while minimising potential issues, we envisage a conceptual framework of Responsible Urban Intelligence (RUI) and advocate an agenda for action. We first define RUI as consisting of three major components including urban problems, enabling technologies, and responsibilities; then introduce transparency, fairness, and eco-friendliness as the three dimensions of responsibilities which naturally link with the human, space, and time dimensions of cities; and further develop a four-stage implementation framework for responsibilities as consisting of solution design, data preparation, model building, and practical application; and finally present a research agenda for RUI addressing challenging issues including data and model transparency, tension between performance and fairness, and solving urban problems in an eco-friendly manner.