We have performed positron annihilation lifetime experiments for stable F-K type icosahedral quasicrystals of Mg-Zn-Y alloys, and besides, we have measured positron annihilation Doppler-broadning spectra by slow variable monoenergetic positron beam in Mg-Zn-Y. In this study, we will discuss the structure of the stable Mg-Zn-Y quasicrystal, taking account of the structural model of a hexagonal phase in Mg-Zn-Y alloy.