Drought index is an important tool for the study of drought, and the construction of comprehensive drought index is the frontier and trend of drought monitoring and risk assessment. Based on Archimedes's Copula function,combined rainfall (Meteorology) and runoff (Hydrology),we constructed a new comprehensive drought index (MSDIp) that can comprehensively characterize the meteorology drought and hydrology drought. It is used to characterize the characteristics of drought evolution in the Weihe River basin. The results indicate that:(1) the MSDIp index can not only capture the occurrence of drought as well as the standardized precipitation index (SPI), but also describe the duration and termination of drought as well as the standardized runoff index (SRI). It possesses the advantages of both meteorological index and hydrological drought index in characterizing drought,which can comprehensively characterize the characteristics of drought evolution. (2) Influenced by climate changing and human activities, the comprehensive drought in the Weihe basin has increased significantly over the past 50 years. (3) There is a change point in the comprehensive drought index sequence of the Weihe basin (1994), and in the future, the risk of drought is increasing. (4) Sunspot and atmospheric circulation anomaly factors have great influence on the occurrence of comprehensive drought in the Weihe basin,of which sunspot activity is the strongest. In addition to the direct influence, sunspot can also influence the occurrence of comprehensive drought by affecting the atmospheric circulation anomaly factors.