A study of the light-meson couplings to the single photon in the framework of the covariant oscillator quark model (COQM) is reported. The transition rates of {ρ(770), b1(1235), a1(1260), a2(1320), π2(1670), ρ3(1690), ρ(1700)}± into π±γ, being expected to be measured by the COMPASS collaboration in their Primakoff-reaction experiments, are calculated. It could be useful not only for understanding the internal structures of observed light-quark mesons and their quark-model classification but also for the ongoing experimental studies by COMPASS.