The amplitude of the El Nino-Southern Oscillation (ENSO) can vary naturally over multidecadal time scales and can be influenced by climate change. However, determining the mechanism for this variation is difficult because of the paucity of observations over such long time scales. Using a 1000-yr integration of a coupled global climate model and a linear stability analysis, it is demonstrated that multidecadal modulation of ENSO amplitude can be driven by variations in the governing dynamics. In this model, the modulation is controlled by the underlying thermocline feedback mechanism, which in turn is governed by the response of the oceanic thermocline slope across the equatorial Pacific to changes in the overlying basinwide zonal winds. Furthermore, the episodic strengthening and weakening of this coupled interaction is shown to be linked to the slowly varying background climate. In comparison with the model statistics, the recent change of ENSO amplitude in observations appears to be still within the range of natural variability. This is despite the apparent warming trend in the mean climate. Hence, this study suggests that it may be difficult to infer a climate change signal from changes in ENSO amplitude alone, particularly given the presently limited observational data.