This study investigates the responses of the Atlantic Meridional Overturning Circulation (AMOC) simulated by the FGOALS-g2 (grid-point version 2 of Flexible Global Ocean-Atmosphere-Land System model) to three different RCPs (Representation Concentration Pathways) of CMIP5 (Coupled Model Intercomparison Project Phase 5). In this investigation, two indices are used: (1) The AMOC index, defines as the maximum value of AMOC between 15°N and 65°N, at depths greater than 500 m, and (2) AMOC extending index, which is the maximum value of AMOC between 15°N and 65°N, and between 2000-m and 2500-m depth. It is found that under RCP2.6 and RCP4.5, both the AMOC index and the AMOC extending index show decreasing trends from 2006 to 2040, following which the AMOC index presents a increasing trend and the AMOC extending index maintains its high value between 2041 and 2100. In contrast, under RCP8.5, rapid decreasing trends are been identified in the time series of both the AMOC index and the AMOC extending index. Through analysis of the mechanism of formation of the North Atlantic deep water, the main component of AMOC, it can be concluded that the long-term trends in AMOC are determined by deep water formation in the Greenland-Iceland-Norwegian (GIN) Seas, while the decadal variability of AMOC is modulated by deep water formation in the Labrador Sea. Meanwhile, it can be shown that due to the stratification stability at around 2000-m depth in the Northern Atlantic Ocean increasing by 30%-40% under RCP2.6 and RCP4.5, the increasing deep water, indicated by the recovering AMOC index, could not sink down any further, which is the reason for the non-recovery of the AMOC extending index.