The development of a city gradually fosters different functional regions, such as educational areas and business districts. In this paper, we propose a framework (titled DRoF) that discovers Regions of different Functions in a city using both human mobility among regions and points of interests (POIs) located in a region. Specifically, we segment a city into disjointed regions according to major roads, such as highways and urban express ways. We infer the functions of each region using a topic-based inference model, which regards a region as a document, a function as a topic, categories of POIs (e.g., restaurants and shopping malls) as metadata (like authors, affiliations, and key words), and human mobility patterns (when people reach/leave a region and where people come from and leave for) as words. As a result, a region is represented by a distribution of functions, and a function is featured by a distribution of mobility patterns. We further identify the intensity of each function in different locations. The results generated by our framework can benefit a variety of applications, including urban planning, location choosing for a business, and social recommendations. We evaluated our method using large-scale and real-world datasets, consisting of two POI datasets of Beijing (in 2010 and 2011) and two 3-month GPS trajectory datasets (representing human mobility) generated by over 12,000 taxicabs in Beijing in 2010 and 2011 respectively. The results justify the advantages of our approach over baseline methods solely using POIs or human mobility.