Abstract: Abstract: Groundwater drought severely impacts social economic development and ecological health. In order to manage groundwater resources scientifically, it is essential to establish a groundwater drought index to provide information for monitoring, management, and drought prediction of groundwater resources. In this study, a groundwater drought index was built by using the standardized groundwater index (SGI) method based on 4 kinds of distribution functions which were Gamma distribution, Beta distribution, lognormal (logN) distribution and generalized extreme value (GEV) distribution. The SGI was derivative of standardized precipitation index (SPI). The kolmogorov-smirnov test (K-S test) was used to determine whether the monthly water level data conformed to the theoretical distribution. If all the functions passed the K-S test, the best fitting distribution was selected by Akaike information criterion (AIC). If the only one passed the K-S test, the function was considered the best. Otherwise, non-parametric method had to be used for SGI fitting. The middle reaches of Heihe river basin was selected as a study case and the data was monthly groundwater level data of 23 wells from 1985 to 2010. The spatial and temporal evolutions of groundwater drought were analyzed in study area. The results showed that the SGI calculated by Gamma distribution and by logN distribution was generally inclined to negative values, indicating that the SGI were skewed towards no drought condition; and the SGI calculated by GEV distribution and by Beta distribution was positively skew, which means that the calculated result was skewed towards drought conditions. Therefore, it was necessary to select the optimal fitting function to calculate SGI for evaluation of groundwater drought by using a series of historical data. In the middle reaches of Heihe river basin, the optimal fitting functions were Beta function and GEV function, which accounted for 78% and 13% of the wells, respectively. The non-parametric method was adopted for groundwater data series of the other 2 wells that did not pass the K-S test. On the whole, the SGI calculated based on the optimal function in different part of study area showed 2 different trends. For example, the SGI showed a trend from decline to rising in Zhangye area while a trend of continuous decline in Linze and Gaotai area, which means that the groundwater drought had been alleviated in Linze and Gaotai. As a derivative of SPI index, SGI index has advantages and disadvantages similar to SPI index. However, due to the inherent periodicity of groundwater level sequences, it is necessary to choose optimal fitting functions to calculate SGI. The non-parametric method has been successfully used in the field of hydrology, and it has an advantage to analyze non-stationary sequences in spite of its limitations of overfitting. Further research should focus on the applicability of SGI in other regions considering the local hydrogeological conditions to find out whether there is a correlation between the optimal fitting function and hydrogeological conditions.