The standardized precipitation index (SPI) and the standardized runoff index (SSI) were calculated using the monthly precipitation and runoff from 1970 to 2016 in central Guizhou, that characterize meteorological and hydrological droughts respectively. The dynamic characteristics of meteorological and hydrological drought in different time scales were analyzed by using run theory, the propagation time of meteorological drought to hydrological drought on different time scales was explored by using cross correlation function and drought propagation threshold. The results showed that: (1) In the past 47 years, the trend of meteorological and hydrological aridity in central Guizhou has been on the rise. The frequency of severe and extreme drought increased, and the characteristics of meteorological and hydrological drought were synchronous in a long time scale; (2) Drought propagation time (PT) was different in different seasons. PTs in spring were 1 to 5 months, PTs in summer were 1 to 3 months, PTs in autumn were 1 to 4 months, and PTs in winter were 1 to 3 months. (3) Under the influence of topography and geomorphology, the PTs of different time scales were different. On the 3-month time scale, the PTs of Yangchang, Gaoche, and Maiweng were 1.36, 2.00, and 1.58 months; on the 6-month time scale, the PTs were 2.75, 2.55, and 3.00 months; on the 12-month time scale, PTs were 3.33, 2.56, and 7.17 months.