The evolution of meteorological drought under global warming is of great significance to drought risk management. Meanwhile, driving factors that influence hydrological factors and water cycle processes play an important role in meteorological drought risk assessment. The Hun-Taizi River basin (HTRB) is a region seriously troubled by drought in China. Therefore, we reveal the evolution characteristics of meteorological drought and its driving factors. First, the standardized precipitation index (SPI) was adopted to characterize the evolution characteristics of meteorological drought. Meanwhile, copula functions with the highest goodness of fit were established to calculate the return period of meteorological drought. Then, the relationships between the SPI and the climatic phenomena were reflected by the cross-wavelet transform method to reveal the driving factors of meteorological drought. The results showed that (1) the meteorological drought of the HTRB varied greatly in different periods, and drought aggravated during spring and autumn; (2) the meteorological drought in the western, northwestern and southeastern regions of the HTRB was characterized by high frequency, short duration and low severity, while that in the other regions was characterized by low frequency, long duration and high severity; (3) the co-occurrence return periods of mild, moderate and severe drought were 1.9, 4.7 and 32.8 years and the joint return periods were 1.5, 3.0 and 9.3 years, respectively; (4) solar activity (sunspot), El Niño Southern Oscillation (ENSO) and Arctic Oscillation (AO) were strongly correlated with drought evolution in the HTRB.