The Lancang–Mekong River Basin (LMRB) is the largest international river in Southeast Asia, supporting a population of about 70 million people. Precipitation is the main source of water resources in the basin, with significant impacts on ecology, production, and livelihoods in the basin. In this study, future precipitation was projected using the Coupled Model Intercomparison Project Phase 6 (CMIP6) climate models. The initial bias of each model was corrected using the daily bias-correction (DBC) method, and then the models were ensembled using the Bayesian model-averaging (BMA) method. The evaluation, based on metrics such as climatology bias, root-mean-square error (RMSE), mean absolute error (MAE), and correlation coefficient (COR), showed that the ensemble precipitation performs better than the individual models. Precipitation under four future Shared Socioeconomic Pathway scenarios (SSP126, SSP245, SSP370, SSP585) displayed an increasing trend throughout the LMRB. The anomalies in annual precipitation in 2061–2090 under each scenario are 136 mm, 142 mm, 114 mm, and 227 mm, in that order. Precipitation in spring and winter shows a trend of increasing in the northern LMRB and decreasing in the southern LMRB, and precipitation in summer and autumn shows a significant trend of increasing in almost the whole basin (significance level 0.05). Spring precipitation in the Mekong Delta decreases in all scenarios. The ratio of wet-season precipitation to dry-season precipitation shows an increasing trend for all scenarios, indicating that the difference between wet-season precipitation and dry-season precipitation will increase in the future. For daily precipitation, the Lancang River Basin (LRB) is dominated by a 3–5% increase in the number of days with 5–10 mm/d of precipitation and the Mekong River Basin (MRB) by a 3–5% increase in the number of days with 10–20 mm/d of precipitation under four SSP scenarios in 2061–2090. There are important changes in the spatial distribution of future precipitation, with the 2500 mm isohyet expanding outwards in a circular pattern and the center of the 1500 mm isohyet moving westwards; i.e., areas with annual precipitation exceeding 2500 mm and 1500 mm will expand. For dry-season precipitation, the 500 mm isohyet shrinks, mainly in a circular pattern towards the center, while the 300 mm isohyet moves mainly towards the east, indicating that areas of dry-season precipitation below 500 mm and 300 mm will expand. In the future, the LMRB will generally become wetter in the wet season and drier in the dry season.