In this report, a technique of single-crystal X-ray diffraction measurements under high pressures, using a diamond-anvil-cell with helium gas as an inert and hydrostatic pressure-transmitting medium, is introduced. The technique has been applied to three-dimensional halogen-bridged mixed-valence gold complexes, Cs₂Au^IAu^IIIX₆ (X=Cl, I) to investigate the mixed-valence state and the crystal structure under high pressures up to 18 GPa and 7. 5 GPa, respectively. The pressure dependences of the unit cell parameters indicate that structural phase transitions occur from tetragonal to cubic at 12. 5 GPa for the Cl-bridged complex, and from tetragonal to monoclinic at 6. 0 GPa for the I-bridged complex. The Cl-bridged complex in the higher pressure phase has a space group, Pm3m and the cubic Perovskite-type structure.