Abstract: Disclosed is a compound semiconductor substrate having a III-V group compound semiconductor layer on a IV group substrate, which has substantially no residual stress and few crystalline defects. The substrate is formed from (a) a IV group substrate, (b) a first III-V group compound semiconductor layer formed on the substrate, (c) a second compound semiconductor layer having such a lattice constant as to produce a stress in a direction opposite to the stress which occurs during the time of forming said first semiconductor layer due to a difference of thermal expansion coefficient between said substrate and said first semiconductor layer, formed on said first semiconductor layer, and (d) a third III-IV group compound semiconductor layer similar to the first semiconductor layer, formed on said second semiconductor layer.