To explore the development mechanism and reduce the loss of droughts, based on standardized precipitation and runoff indices, the meteorological drought to hydrological drought propagation characteristics in the Jinsha River Basin were revealed from the perspective of causality using the convergent cross mapping method. The drought propagation characteristics under future climate scenarios were predicted using the CMIP6 climate model. The results show that the drought propagation time in the Jinsha River Basin during the historical period from 1985 to 2014 was one month and six to eight months in wet and dry seasons, respectively. The propagation rate in wet season during the historical period was larger(0.90~0.97) than that in dry season (0.89~0.93), and it was the largest at Pingshan Station, followed by that at Shigu Station, and lowest at Xiaodeshi Station. The drought propagation time in the future from 2030 to 2089 in the basin will have little change during wet season, but have a significant spatial difference during dry season, and it will be shortened by one month at Shigu and Pingshan stations in the mainstream, while be extended by one to two months at Xiaodeshi Station in the tributary. The drought propagation rate in the future will increase in the basin, with a small increase in wet season (2.50%~9.83%) and a large increase in dry season (5.82%~11.72%). In terms of spatial distribution, Xiaodeshi Station will have a larger increase in the drought propagation rate in the future, followed by Shigu Station, and Pingshan Station will have the smallest increase. Moreover, the differences in the increase of drought propagation rates between different climate scenarios will be relatively small in the future.