Case study with the October-MJO and November-MJO during the DYNAMO/CINDY period have been conducted to show that the former is largely controlled by internal dynamics, while the later strongly rely on active air-sea interaction. In order to understand the diversified responses of models to air-sea interaction, a series of hindcast experiments were carried out with the NCEP GFS under three different SST forces (Climatology, NCDC, and TMI) with three different cumulus parameterizations (RAS, SAS, SAS2) during DYNAMO/CINDY period. It is found that model MJO responses to air-sea interaction strongly depend on the accuracy of the intraseasonal SST anomaly and the sensitivity of cumulus parameterizations to underlying SST forcing. Pathway on further understanding the diversified effects of air-sea interaction on the MJO will be discussed too.