Groundwater quality assessment is important for understanding the suitability of groundwater resources for various purposes. Although many different methods have been proposed for this purpose, few methods have considered the spatial variation of groundwater components during the assessments. In this study, we proposed to combine the self-organizing map (SOM) and entropy-based weight determining method to assess groundwater quality. Totally, 955 water samples taken from 58 wells during 2010–2017 were used in the study. 22 hydrochemical components (K+, Na+, Ca2+, Mg2+, NH4+, Cl−, SO42-, F−, NO3−, Fe2+, Fe3+, Al, etc.) were used in the assessment for each sample. These sampling points can be classified into five clusters, which may be affected by four different sources: landfill sources (cluster 3), industrial and agricultural sources (cluster 5), and domestic sewage discharge sources (clusters 1, 2, and 4). The scores of the water quality of the five clusters that were calculated by the entropy method are 0.2658, 0.2634, 0.5737, 0.2608, and 0.5718, indicating that the groundwater affected by domestic sewage discharge sources (clusters 1, 2, and 4) are better than other two sources (clusters 3 and 5) in the study area. The results of this study provide insights for the protection of groundwater resources and the treatment of groundwater pollution in the future.