The spectra of luminescence and magnetic circular polarization of luminescence of praseodymium–yttrium aluminum garnet Pr3+ : Y3Al5O12 (PrYAG) are studied in the visible spectral region at temperature T = 300 K. An analysis of spectral dependences of magnetooptical and optical spectra makes it possible to identify optical 4 f–4 f-transitions between Stark sublevels of multiplets 3P0, 3P1, 3Н5, and 3Н6 in PrYAG. It was shown that an important role in the spectrum of the degree of magnetic circular polarization of luminescence of this paramagnetic garnet is played by the effect of quantum-mechanical J–J mixing of states of Stark singlets 3Н5 and 3Н6 of non-Kramer rare-earth ion Pr3+ in the “green” luminescence band related to forbidden 4 f → 4 f transition 3P0 → 3Н5 in the visible spectral region. To interpret the spectra of magnetic circular polarization of luminescence, the energy of experimentally determined Stark sublevels of multiplets under study, their irreducible representations and wave functions determined by numerical simulation of the energy spectrum of the rare-earth ion Pr3+ in the garnet structure are used.