Groundwater drought is a critical factor affecting vegetation develoment in semi-arid sandy regions. Located in the arid and semi-arid zone of northern China, the Maowusu Sandland relies on groundwater resource management for its enduring sustainable development. However, the scarcity of direct groundwater observations across spatial and temporal dimensions presents challenges for the quantitative assessment of groundwater drought. Based on the observed data of the Global Land Data Assimilation System (GLDAS), this study aims to explore the changing patterns of groundwater storage by utilizing Gravity Recovery and Climate Experiment (GRACE) satellite data to invert the dynamic changes in groundwater storage in the Maowusu Sandland from 2002 to 2021. To quantitatively analyze the regional groundwater drought conditions, the study constructs a groundwater-level estimation index and refines it as the GRACE Groundwater Storage Index (GGSI). This paper first selects four different distribution functions and choose the optimal distribution function by the KS test, then calculate the GGSI in different time scales to quantitatively analyze groundwater drought. Subsequently, the correlation coefficients between GGSI and precipitation are calculated to reveal the lag effect of groundwater drought. Finally, the time lag analysis of GGSI and SPI is carried out. The key findings are as follows: 1) Different fitting functions have different responses to the data fitting results, and the best fitting function for this study area is the Pearson III function, which can more accurately reflect the trend of the groundwater storage in this area; 2) From 2002 to 2021, the GGSI exhibited fluctuating changes, with trends becoming more apparent as the time scale increases, showing an overall stable trend of initial increase followed by a decrease. The onset, conclusion, and severity of drought varied across different time scales, but the drought periods were generally consistent. The years 2007 and 2021 were identified as drought years in the Maowusu Sandland; 3) The consistent delay between drought and precipitation in this area spans from 5 to 8 months, with significant correlations observed within both of these lag periods.