Land surface water is a key part in the global ecosystem balance and hydrological cycle. Remote sensing has become an effective tool for its spatio-temporal monitoring. However, remote sensing results exemplified in so-called water indices are subject to several limitations. This paper proposes a new and effective water index called the Sentinel Multi-Band Water Index (SMBWI) to extract water bodies in complex environments from Sentinel-2 satellite imagery. Individual tests explore the effectiveness of the SMBWI in eliminating interference of various special interfering cover features. The Iterative Self-Organizing Data Analysis Technique Algorithm (ISODATA) method and confusion matrix along with the derived accuracy evaluation indicators are used to provide a threshold reference when extracting water bodies and evaluate the accuracy of the water body extraction results, respectively. The SMBWI and eight other commonly used water indices are qualitatively and quantitatively compared through vision and accuracy evaluation indicators, respectively. Here, the SMBWI is proven to be the most effective at suppressing interference of buildings and their shadows, cultivated lands, vegetation, clouds and their shadows, alpine terrain with bare ground and glaciers when extracting water bodies. The overall accuracy in all tests was consistently greater than 96.5%. The SMBWI is proven to have a high ability to identify mixed pixels of water and non-water, with the lowest total error among nine water indices. Most notably, better results are obtained when extracting water bodies under interfering environments of cover features. Therefore, we propose that our novel and robust water index, the SMBWI, is ready to be used for mapping land surface water with high accuracy.