We extensively explore the high-pressure structures of InBi by using a newly developed particle swarm optimization algorithm.An orthorhombic Imma structure is discovered to be stable from 43.7 GPa to 107.9 GPa,ruling out the previously speculated cubic structure.Further increasing the pressure,we find a tetragonal P4/nmm structure which is energetically more favourable from 107.9 GPa to 200 GPa.Especially,the tetragonal P4/nmm structure is known to occur at high pressure in the structures of ZnO and MgTe.We also predict this structure to be a high-pressure structure of ZnTe.Thus the tetragonal P4/nmm structure may be a universal high-pressure structure of the II-VI and the III-V compounds.