This study focuses on the bias of the multimodel ensemble mean in the precipitation simulated using models of the fifth phase of the Coupled Model Intercomparison Project (CMIP5) compared with the precipitation data using Climatic Research Unit Timeseries version 4.0 (CRU TS v4.0). Three bias correction methods are tested, and a precipitation projection with the correction is made for the coming 30 years (2021–2050) based on the selected 20 CMIP5 models. Results show that the precipitation in the CMIP5 historical simulation is overestimated in northern Asia and underestimated in the south for 1960–2005 with 30%–40% more precipitation than that observed in the Tibetan Plateau, Inner Mongolia, and Mongolia; 20%–30% less in the South China Coast and Vietnam; and 30%–40% less in South Asia than that of the observation. The bias pattern of the projected precipitation for 2006–2015 under the Representative Concentration Pathway (RCP) 4.5 scenario is found to be similar to that from the CMIP5 historical climate simulation, implying that the bias pattern is almost stationary and should belong to the model climate drift that can be removed using the difference between the period-mean projection and historical simulation. However, this bias correction leads to a much small magnitude of the precipitation anomaly, although it has a good anomaly rate compared with the observation. The bias correction test confirms that the performance of the bias correction using logarithm regression (LR) is better in northern Asia compared with the year-to-year increment regression (YYIR) during the warm season (May–October). Meanwhile, the YYIR is better than the LR in southern Asia in this season. Nevertheless, the LR is better in the south, and YYIR is better in the north during the cold season (November throughout next April). Therefore, combining the two regression methods can form a regional combination bias correction. The regional combination method is applied in the bias correction for the 2021–2050 precipitation projection of the Asian continent under the RCP4.5 scenario, in which an additional bias correction of climate drift removal is added in the blind areas in the two bias corrections. The projection for the warm season shows more or less changes in the precipitation pattern compared with that of 1976–2005, such as the 10%–20% decrease in precipitation in the Southern China, the northeastern part of South Asia, south part of Central Asia, and northeastern Arabian Peninsula. The projected precipitation would increase to approximately 20% in the belt from the Three-River-Source area throughout the Huaihe delta area, 10% increase in the southern part of Northeast China, 10% and 20% increase in northern and southern Xinjiang, respectively, 10% or 20% decrease in North China and most of Northeast China, and 10% increase in northern Indo–China Peninsula, in addition to a minor increase in precipitation in the high latitude of Asia. In the cold season, the projected precipitation would increase in the north and decrease in the south of Asia, such as the 10% decrease in South Asia, 5% decrease in Southwest China, 20%–40% increase in West China, 5% increase in North and Northeast China, and 10%–40% increase in the high latitude of Asia. Consequently, there would be more precipitation with potential floods in the upper reaches of the Yangtze River and Yellow River over the next 30 years, whereas the drought would possibly continue in Southwest China as it has experienced for the last decade. These will provide suggestions for the relevant department of the local government to take advance measures concerning the risks of flood and drought in the context of climate warming.