This paper presents numerical studies on the vortex-induced motions (VIM) of a deep draft semisubmersible platform with four square columns based on improved delayed detached-eddy simulation (IDDES). The in-line, transverse and yaw motions for 0°, 22.5° and 45° current incidences are studied. The effect of draft and rounded corners of columns on the VIM is investigated. It is found that the present results agree well with the experimental data. The different lock-in regions in VIM of a semi-submersible are observed for 0°, 22.5° and 45° current incidences. The lock-in behavior occurs at 6.0< Vr< 8.0 for both 22.5°and 45°current incidences, while it lags for 0° current incidence. However, yaw motions tend to monotonically increase with the growing reduced velocities for all current incidences at 3.0< Vr< 13.0. The more rounded edges of columns in which four edges per column are rounded can lead to a significant increase in transverse and yaw motions. However, the characteristic amplitudes for transverse motions and yaw characteristic amplitudes change slightly with the growing corner radii of columns in which only one edge per column is rounded. The transverse and yaw motion increase with the draft, and the lock-in behaviour is not observed at the lower draft condition (H/D ≤ 0.9). © 2021, Editorial Board of Journal of Ship Mechanics. All right reserved.