The Copula theory was used to construct the joint distribution of precipitation in the flood season, the dry season，and the whole year between the water source area and the water receiving areas in the middle route of the SouthtoNorth Water Transfer Project. The effect of climate change on the synchronous-asynchronous encounter probability of rich-poor precipitation was analyzed based on the General Circulation Models (GCMs) outputs in the IPCC Fourth Assessment Report(IPCC AR4). The results show that on the flood season scale, the synchronous frequency of both rich and poor exhibits increasing tendency in the Han-Tang(Hanjiang Water Source Area-Tangbaihe Water Receiving Area) encounter and Han-Hai(Hanjiang Water Source Area-Hai River Water Receiving Area) encounter, and the values are 3.34%~16.48% and 2.56%-8.21%, respectively, under different emission scenarios; while the synchronous frequency of both rich and poor exhibits decreasing tendency in Han-Huang(Hanjiang Water Source Area-Yellow River Water Receiving Area) encounter, the value is in the range of -1.97%-9.57% under different emission scenarios. On the dry season scale, the synchronous frequency of both rich and poor in the Han-Tang encounter and Han-Hai encounter decreases about -0.21%-9.42% and 0.99%-5.54%, respectively，while that in Han-Huang encounter increases about 1.79%-13.28%. On the annual scale, the synchronous frequency of both rich and poor exhibits decreasing tendency in all the three encounters, and the values for the Han-Tang, Han-Huang, and Han-Hai encounters decrease about -2.88%-10.97%, -1.28%-5.05%, and -2.33%-7.01%, respectively.