Accurately identifying and delineating urban functional areas has seen increasing demand in smart urban planning, landscape design, and resource allocation. Recently, POI (point of interest) data have been increasingly applied to identify urban functional areas. However, heterogeneity in urban spaces or the corresponding POI data has not been fully considered in previous studies. In this study, we proposed a new scheme for urban-functional-area identification by combining POI data, OpenStreetMap (OSM) datasets, and high-resolution remote-sensing imagery. A function-intensity index that integrates the quantitative-density index and average-nearest-neighbor index (ANNI) of POIs was built for representing the urban function. The results show that the proposed function-intensity index can balance the impact of the spatial heterogeneity of each type of POI on determining the functional characteristics of the urban units. In Futian District, Shenzhen, China, the method was effective in distinguishing functional areas with fewer POI amounts but high ANNIs from those functional areas with dense POIs. The overall accuracy of the proposed method is about 11% higher than that of the method using the POI density only. This paper argues for considering both the quantitative density and spatial heterogeneity of POIs to improve urban-functional-area identification.