The amount of winter precipitation over southeast China (SCWP) is significantly affected by the El Niño-Southern Oscillation (ENSO), with generally an enhanced SCWP response to El Niño events. In this paper, we find that this relationship shows remarkable nonstationarities on the multidecadal timescale. Running ENSO-SCWP correlation maintains statistically significant before the mid-1960s and after the mid-1990s but not during the interim period, which exhibits an approximate synchronized temporal evolution with the Atlantic Multidecadal Oscillation (AMO). A statistical method for interpreting nonstationary relationships is then applied to quantitatively verify and measure this possible AMO modulation. It is demonstrated that the nonstationary ENSO-SCWP correlation can be expressed to a large extent by the influence of the AMO-ENSO nonlinear effect (AMO*Niño3.4) on the SCWP. This influence intensifies the ENSO-SCWP relationship during the positive AMO phase but weakens it during the negative AMO phase. Therefore, the nonstationarity in the ENSO-SCWP relationship comes predominantly from an AMO modulation via this key nonlinear effect. We further suggest that a positive AMO favours a westward shift of ENSO sea surface temperature (SST) anomaly pattern in the tropical Pacific. Correspondingly, the anomalous western North Pacific (WNP) anticyclone also migrates westward, which gives rise to pronounced moisture transports and vertical motions over the adjacent southeast China, thereby resulting in a significant ENSO-SCWP relationship. In contrast, during the negative AMO phase, the eastward-shifted ENSO SST and WNP anticyclonic anomalies produce significant atmospheric anomalies primarily to the east of the Chinese mainland, thus having less effect on the SCWP.