Drought is a complex phenomenon caused by lack of precipitation that affects water resources and human society. Groundwater drought is difficult to assess due to its complexity and the lack of spatio-temporal groundwater observations. In this study, we present an approach to evaluate groundwater drought based on relatively high spatial resolution groundwater storage change data. We developed an artificial neural network (ANN) that employed satellite data (Gravity Recovery and Climate Experiment (GRACE) and Tropical Rainfall Measuring Mission (TRMM)) as well as Global Land Data Assimilation System (GLDAS) models. The Standardized Groundwater Level Index (SGI) was calculated by normalizing ANN-predicted groundwater storage changes from 2003 to 2015 across South Korea. The ANN-predicted 25 km groundwater storage changes correlated well with both the in situ and the water balance equation (WBE)-estimated groundwater storage changes, with mean correlation coefficients of 0.87 and 0.64, respectively. The Standardized Precipitation–Evapotranspiration Index (SPEI), having an accumulation time of 1–6 months, and the Palmer Drought Severity Index (PDSI) were used to validate the SGI. The results showed that the SGI had a pattern similar to that of SPEI-1 and SPEI-2 (1- and 2-month accumulation periods, respectively), and PDSI. However, the SGI performance fluctuated slightly due to its relatively short study period (13 years) as compared to SPEI and PDSI (more than 30 years). The SGI, which was developed using a new approach in this study, captured the characteristics of groundwater drought, thus presenting a framework for the assessment of these characteristics.