A detailed study of molecular beam epitaxy of GaAs on homemade SiGe substrates has been performed. It was found that the initial migration-enhanced epitaxy process with As prelayer is crucial to obtain high-quality GaAs. By (004) x-ray diffraction, the lattice mismatch between GaAs and SiGe was demonstrated to be reduced compared with the conventional GaAs/Ge heterostructure. Furthermore, narrower halfwidth of the rocking curve and stronger photoluminescence intensity were found for GaAs on SiGe. These results show that SiGe is a promising material as an alternative substrate to Ge to realize exact lattice matching to GaAs for solar cell applications.