Affected by global climate change, the status of meteorological and hydrological drought in the Lancang-Mekong River basin (LMRB) has witnessed great changes. Therefore, predicting the temporal and spatial variations of future drought as well as its propagation characteristics has become the basis for tackling climate changes and conducting cooperation on the water resources of the Mekong River. By applying the SWAT model and the method of atmosphere-land coupling, both the history (1960-2005) and the future (2022-2050 and 2051-2080) hydrological processes of the LMRB were simulated. Moreover, the future temporal and spatial variation trends of meteorological and hydrological drought were also predicted and analyzed by using the Standardized Precipitation Index and Standardized Runoff Index. The research results indicated that: ① In the future, the amount of precipitation will be increased. Thus, the meteorological drought will be alleviated to some extent, but at the same time, the inhomogeneous distribution of intra-annual precipitation and increased evaporation from the river basin together will cause a severer hydrological drought and an intense propagation process. ② Hydrological drought will have significant spatial heterogeneity. Specifically, the hydrological drought will be the most intense in Jinghong and Chiang Saen stations, followed by Luang Prabang, Mukdahan, and Pakse stations, and be the weakest in Vientiane station. ③ Over time, the frequency of hydrological drought in the river basin will be slightly decreased, but the proportion of heavy drought and severe drought will be increased, and the extreme drought will be enhanced both in amount and strength. Furthermore, the features of spatial variation will be more significant and noticeable.