The diurnal variability of sea surface temperature (DV SST) can significantly affect the air-sea fluxes during the suppressed phase of the MJO, and thereby the development of convection that leads to the active phase of the MJO. The DV SST during the suppressed phase of three MJO events from 2007 to 2009 is simulated using a global coupled model, ACCESS-S1, assuming the atmosphere-ocean coupling frequency (CF) of 1 h. Compared with the v2 MTSAT-1R satellite SST measurements, the model underestimates SST observations by ~ 1 °K in the morning (9 am－12 pm), and overestimates by ~ 0.5 °K in the evening (7 pm－12 am). Different DV SST will affect the magnitude and phase of air-sea fluxes and moisture. We discuss the factors to the DV SST. Changing the CF ≤ 6 h affects the peak SST by only < 0.2 °K. Mixing the upper 10 m ocean artificially during the model simulations can underestimate the peak SST by > 1 °K. That is, the vertical resolution of 1 m is more important than the high coupling frequency, and is required for simulating the thermal stratification during the diurnal warming. Accurately simulating the magnitude and phase of DV SST will be crucial to the future forecast on the evolution of MJO events.