A dual dispersive x-ray (DDX) diffraction system which combines energy dispersive x-ray (EDX) diffraction with angle dispersive x-ray (ADX) diffraction has been developed on the cubic-type multianvil press named MAX80 at the beamline NE5C at the TRISTAN Accumulation Ring (6.5 GeV) of the Photon Factory. With the DDX diffraction system, quick recording of the diffraction pattern is made in the EDX diffraction mode for pressure determination and sample identification, and high-quality diffraction patterns with reliable diffraction intensities are obtained in the ADX diffraction mode for structure analysis. It requires only three minutes to switch between the EDX and ADX diffraction modes. The structure relation between Bi iii and Bi iii′ which was suggested by previous researchers has been investigated with this system. The volumetric compressibility was obtained by the EDX diffraction mode and the atomic arrangement was determined from the data collected in the ADX diffraction mode. No significant change was found around the suggested transition pressure. The crystal structure of Bi iii′s is therefore determined to be identical to that of Bi iii.