We searched for plausible crystal structures and the entailing electronic profiles of highly-compressed Sb using an originally developed structure-search method and first-principles calculations based on the density functional theory. We report that the experimentally observed highest-pressure (59 GPa) close-packed body-centered cubic (bcc) structure remains the lowest-enthalpy structure at least up to 1000 GPa within the precision of our calculations. Any possibilities of complex structures with many atoms and distortions within the bcc phase, as in the case of the cI16 structure observed for high pressure P, were also safely ruled out. Careful investigations of the density of states (DOS) and phonon dispersions revealed that the bcc structure becomes more stable with increasing pressure. The DOS and phonon dispersions indicate that the stability of the bcc phase increases with increasing pressure. In understanding the strong stability of this stubborn bcc phase, we discuss the phonon and electronic profiles of Sb.