We report joint theoretical and experimental research on the high-pressure structures of bismuth selenide (Bi2Se3) up to 50 GPa. Our first-principles structure prediction via calypso methodology meets our high-pressure X-ray diffraction experiments performed in diamond anvil cell. We established that the ambient-pressure rhombohedral phase transforms to a monoclinic C2/m structure at 9.8 GPa, and then to a monoclinic C2/c structure at 12.4 GPa. Above 22.1 GPa, we were able to identify that Bi2Se3 develops into a novel 9/10-fold structure, which was not taken by its other family members Bi2Te3 and Sb2Te3. The large differences in atomic core and electronegativity of Bi and Se are suggested to be the physical origin of the stabilization of this 9/10-fold structure. Our research work allows us to reveal a rich chemistry of Bi in the formation of 6, 7, 8, and 9/10-fold covalent bond with Se at elevated pressures.