Surface water bodies play important roles in socioeconomic development and ecosystem balance. The fast-developing technology of remote sensing offers opportunities for the automatic extraction and dynamic monitoring of surface water bodies. Compared with other medium- and low-spatial-resolution remote sensing images, such as Landsat and MODIS, Sentinel-2 imagery provides higher spatial resolution and revisit frequency, making it more suitable for surface water extraction. The existing research works on surface water extraction using Sentinel-2 imagery remain focusing on the construction of water indexes, which is easily affected by shadows and built-up areas. In this study, we propose an automated surface water extraction method based on the presence and background learning algorithm (ASWE-PBL) using Sentinel-2 imagery and OpenStreetMap (OSM) data. The OSM data are used as the auxiliary data to automatically select water samples, and the PBL algorithm is adopted to predict the water presence probability. ASWE-PBL is validated using six typical study areas in China, and the modified normalized difference water index, the automated water extraction index, and the random forest classifier are employed for comparison. Moreover, feature optimization, parameter sensitivity, computation cost, and future work are analyzed and discussed. The experimental results show that ASWE-PBL can effectively suppress noise caused by shadows and built-up areas and can obtain the highest kappa coefficient for five study areas but not for Guangzhou and that the ten-spectral-band composite of Sentinel-2 imagery is a better feature combination scheme than that of spectral and water indexes.