Abstract: The inherent law and mechanism, underlying the complex ocean currents in sea, can offer scientific support for marine engineering, such as search and rescue at sea, pollutant diffusion forecast, shipping route design. In this paper, the generalized cell mapping method based on the idea of space discretization is proposed to carry out the global analysis for finding long-term and short-term dynamic structures underlying the Indian Ocean. Taking the typical monsoon and climate features in the ocean region into account, the one step transition probability matrices in different interval levels are created based on the drifter database from 1979—2019 to describe the evolutions of state of the system. Then, the long-term and short-term profiles of attraction (vortex core) and its region of influence (vortex area) are revealed and characterized by means of topological analysis. In comparison, the predicted distributions and features of responses are highly consistent with real observations of drifters to verify the rationality and validity of the proposed method and results. It is shown that the long-term vortex area is obviously presented in the region of latitude 20° to 45° south, longitude 40° to 96° east, which causes the dynamic concentration of drifters on the region, while the repellency for drifter trajectories is also observed both near the south of latitude 40° south and the equator. Meanwhile, the short-term dynamic vortices can dominate transient paths and tendency of drifters to induce the counterclockwise circulation of current in the southern Indian Ocean.