The ternary mixed crystal on interband optical absorption coefficients in wurtzite MgxZn1−xO/ZnO/MgyZn1−yO asymmetric quantum wells have been investigated and shows that the IOAC peak decreases rapidly and presents a blue shift with the increment of Mg component x. Size effect on interband optical absorption coefficients in wurtzite MgxZn1−xO/ZnO/MgyZn1−yO asymmetric quantum wells have been investigated and shows that the absorption peak is more sensitive to the change of the well width than the left barrier size. The built-in electric field and Poisson potential are considered in calculation of theeigenstates and eigenenergies of electrons and holes. Our results could give guidance to the experiments in optical switching and optical communication.