Rhombic triacontahedral-type icosahedral quasicrystal and its 1/1- and 2/1-approximants in an Al-Mg-Zn alloy system were systematically studied by means of positron-annihilation measurements. The structural vacancy densities, average positron diffusion length, average positron diffusion length in the vacancy-free region, positron diffusion coefficient, and positron mobility were successfully derived. The results indicated that the thermarized positrons in the vacancy-free region tend to localize as the order of the approximant increases.