A weighting ensemble method (WEM) by pattern correlation coefficients (PCC) in sliding windows (SWPCC) (WEMSWPCC) is proposed according to distinct pattern differences among simulation performances of Intergovernmental Panel on Climate Change (IPCC) Fourth Assessment Report (AR4) (IPCC-AR4) 22 coupled models for Asian summer monsoon precipitation in the late 20th century under scenario 20C3M (20th century climate coupled models simulations). By comparing the distributions of SWPCC and the distributions of simulations of 22 models, it is shown that the SWPCC can quantitatively reflect the pattern differences in each regional window among these models. Furthermore, the comparisons among the ensemble simulations with various ensemble methods and the observed result, it is also shown that the ensemble simulation of Asian summer monsoon precipitation in the late 20th century with the WEMSWPCC proposed in this paper is better than both that with the simple multi-model ensemble method (SMMEM) and that with the traditional pattern correlation coefficients (TPCC) weighting ensemble method (WEMTPCC). For this reason, the WEMSWPCC ensemble method is applied to the ensemble predictions of the evolution trend of Asian summer monsoon precipitations for various periods of the 21st century under the A1B emission scenario by IPCC-AR4 22 coupled models. The results show that under the A1B emission scenario, the South Asian summer monsoon precipitation in the middle period of the 21st century (2045－2065) will be significantly stronger than that in the late period of the 20th century, while the East Asian summer monsoon precipitation anomalies will exhibit a meridian tripole pattern distribution from the south to the north in the middle period of the 21st century as compared with those in the late period of the 20th century. That is, the summer monsoon precipitation in North China and South China will obviously increase in comparison with that in the late period of the 20th century, but it has not obvious change in the Yangtze River valley, compared with that in the late period of the 20th century. Moreover, the results also show that this evolution trend of Asian summer monsoon precipitation may continue to the late period of the 21st century.