The major problems of the GaAs/Si heteroepitaxy are the high density of threading dislocations and the high residual strain in the GaAs epilayers. The residual strain in the epilayer is attributed to the difference in contraction during cooling down from the growth temperature. It was reported previously that the residual stress in GaAs epilayer could be reduced by reducing the growth area using substrate patterning. In this paper, we report a new approach to grow strain- free GaAs layer on Si substrates. The residual strain in GaAs/Si is tensile in nature, therefore we attempted to compensate this thermally induced strain by compressive lattice mismatched strain. The thermally induced strain in the GaAs layer was successfully compensated by the lattice- mismatch induced strain using In0.032Ga0.968As. By that method, we could grow thin strain- free GaAs layers on Si without patterning. The strain relieving effect was confirmed by photoluminescence experiment.