SiGe/silicon-on-insulator (SOI) prepared by epitaxial growth of SiGe layer on separation by implanted oxygen SOI wafer is used to fabricate the SiGe-on-insulator (SGOI) by the multistep Ge condensation technique. The SGOI with various Ge content is systematically studied by employing Auger electron spectroscopy, X-ray diffraction, Raman spectroscopy, and atomic force microscopy. During the condensation processes, the degree of strain relaxation increases at the very beginning through the generation of misfit dislocations at elevated temperature. And then, the degree of strain relaxation starts to decrease with the reduction of SiGe thickness on the insulator although Ge content continues to increase. At this stage, the increase of density of misfit dislocations cannot effectively relieve the strain and the strain relaxation is dominated by the reduced thickness. When the Ge content in the SGOI is up to 0.58, the surface roughening starts to play a role in relieving the strain accumulated in the thinner SiGe layer with higher Ge content.