We report a simple method to produce a single crystal region of an inverse bicontinuous cubic (QII) phase of a lipid, 1-monoolein. By starting with the lipid of the sponge (L3) phase in the presence of 1,4-butanediol, we can obtain a single crystal region of the double-diamond QII phase in 1 week by controlled dilution of 1,4-butanediol. The length of the single crystal region in a 0.5 mm diameter capillary was on the order of millimeters. X-ray diffraction images of the region showed diffraction "spots", but not "rings" as in powder diffraction. The diffraction images also changed rotation angle dependently. We could assign Miller indices to all of the distinguishable diffraction spots from the region. This method would bring benefits to the basic and applied research areas of the Q phases.