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The Wei River Basin, a typical arid and semi-arid region, is frequently attacked by droughts, which heavily limits its sustainable development of society and economy. Therefore, the main motivation of this study is to investigate the drought evolution characteristics and risk evaluation in the basin, which is crucial for drought warning, water resources management as well as agricultural development. The modified Mann-Kendall test trend method was used to capture the trend of the severity and duration of historical drought events, and the persistence of droughts was analyzed based on the Rescaled Range (R/S) analysis. Additionally, the Morlet wavelet analysis was utilized to calculate the period of dry and wet condition, and copulas were applied to calculate the joint return period of two typical scenarios. The main results are as follows: (1) the whole basin has an obviously dry trend, especially in autumn and winter; furthermore, the months with a wet trend are primarily concentrated in July and August; (2) the persistence of droughts is strong, indicating that droughts in the near future may be persistent; (3) the average "or" and "and" joint return periods under scenario (1) where drought duration is 6 months and drought severity is 4 are approximately 15.6 and 28.9 years, respectively, while those under scenario (2) where drought duration is 8 months and drought severity is 6 are approximately 34.9 and 53.1 years, respectively. In general, the drought risk of the northwestern basin is larger than that of the southeastern basin.