Locally dislocation-free SiGe-on-insulator is fabricated by chemical vapor deposition. Lateral selective SiGe growth of ~30, ~45 and ~55% is performed around ~1 µm square Si(001) pillar located under the center of a 6.3 µm square SiO₂ on Si-on-insulator substrate. In the laterally grown SiGe, tensile strain is observed and the strain is slightly increased at the corner of the SiGe. Ge incorporation is influenced by the strain and facet orientation. These phenomena are pronounced for SiGe with higher Ge content. The dislocation-free area is formed along <010> from the Si pillar by lateral aspect-ratio-trapping.