The invention provides a manufacturing method of silicon germanium on insulator (SGOI) or strained silicon on insulator (sSOI) with high relaxation and low defect density. According to the method, firstly, ion implantation is carried out on the surface of single crystal used as a substrate, and then multiple material layers containing superlattice structures formed by Si1-xGex/Ge or Si/Si1-xGex are formed; secondly, after Si1-yGey and/or Si grows at a low temperature on the structure surfaces of the formed multiple material layers, annealing process is carried out to enable a relaxation phenomenon to happen on a surface Si1-yGey layer; and finally, an intelligent peeling technology is used for transferring at least a part of layers in the structure where the relaxation phenomenon happens to the oxygen bearing layer surface of an oxygen-bearing substrate to form the SGOI or sSOI structure. Therefore, waste of an existing super-thick buffering layer in material and time can be effectively avoided, and influence of a first-growth after-implantation method on an epitaxial layer is avoided.