The mechanism associated with the modulation of ENSO amplitude caused by the Atlantic Multi-decadal Oscillation (AMO) is investigated by using a long-term historical observational data and various types of models. The observational data for the period 1900-2013 show that the positive phase of AMO has accompanied cooling in the central tropical Pacific and weak ENSO variability and vice-versa in the negative phase. Such a relationship between the AMO and ENSO amplitude has been reported by a number of previous studies. In the present study, we demonstrate that the weakening of the ENSO amplitude during the positive phase of AMO is related to the changes of the SST cooling in the eastern and central Pacific in the presence of warm poor in the Western Pacific, which were reproduced reasonably well by CGCM simulations.