In order to obtain high-quality single grains of the Al-Cu-Ru icosahedral quasicrystal (iQC), suitable for a structure analysis, the crystal growth conditions with the self-flux method have been studied. The melts of the master alloys with the compositions of Al57.0+xCu39.5-xRu3.5 (x = 0, 2.5, 5, 7.5, 10) and Al62.0Cu34.0+y Ru4.0-y (y = 0, 0.5, 1.5) were held at 1150°C for 2 h, then cooled down to 800, 900, or 1000°C at a rate of −2 K/h, and subsequently retained for various durations, up to 750 h. Single grain iQCs having several millimetre-sizes, which were evaluated their quality by powder X-ray diffraction (XRD), were grown throughout this study. The peak of (664004) reflection in powder XRD of the iQCs grown at 1000°C has approximately 50% narrower width than that grown at 800°C. The inhomogeneity of the compositions intra- as well as inter-grains grown at 800°C was observed. High-quality single grains with homogeneous composition could be achieved with a long-time annealing at 900°C or regardless of the annealing time at 1000°C. By changing the Al/Cu ratio of the master alloys, the composition could also be controlled for the iQCs grown at 1000°C. Single-crystal XRD experiment with synchrotron radiation on Al66.6Cu16.4Ru17.0 iQC, grown at 1000°C, resulted in the collection of 2680 independent Bragg reflections that confirms the high-quality of the sample. The phase retrieval of the diffraction data resulted successfully in obtaining the structure solution, which reveals some characteristic features of this face-centred iQC structure.