The Complex EOF (CEOF) analysis was carried out in order to study the interannual and interdecadal variations of the coupled circulation of atmosphere and ocean in the tropical Indian Ocean and unveil their relationship with the Indian Ocean dipole (IOD) and ENSO. The results show that: In the same mode, the anomalous current of ocean is equatorial-trapped, but the wind field has no such phenomena; the first mode has a close relationship with the IOD, the second mode counts much on ENSO; the atmosphere field of the first and second modes represents the abnormal changes of Walker circulation; the interannual variation of the Indian Ocean's temperature lies mainly on the coupled state of atmosphere and ocean about the Indian Ocean, but the ENSO circulation of the Pacific Ocean also has some influence.