The spectra of luminescence and magnetic circular polarization of luminescence of praseodymium–yttrium aluminum garnet Pr^3+ : Y_3Al_5O_12 (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 ^3 P _0, ^3 P _1, ^3 Н _5, and ^3 Н _6 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 ^3 Н _5 and ^3 Н _6 of non-Kramer rare-earth ion Pr^3+ in the “green” luminescence band related to forbidden 4  f → 4  f transition ^3 P _0 → ^3 Н _5 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 Pr^3+ in the garnet structure are used.