The large radiative production rate for pseudoscalar mesons in the J/ψ radiative decay remains elusive. We present the first lattice QCD calculation of partial decay width of J/ψ radiatively decaying into η_{(2)}, the SU(2) flavor singlet pseudoscalar meson, which confirms QCD U_{A}(1) anomaly enhancement to the coupling of gluons with flavor singlet pseudoscalar mesons. The lattice simulation is carried out using N_{f}=2 lattice QCD gauge configurations at the pion mass m_{π}≈350 MeV. In particular, the distillation method has been utilized to calculate light quark loops. The results are reported here with the mass m_{η_{(2)}}=718(8) MeV and the decay width Γ(J/ψ→γη_{(2)})=0.385(45) keV. By assuming the dominance of U_{A}(1) anomaly and flavor singlet-octet mixing angle θ=-24.5°, the production rates for the physical η and η^{'} in J/ψ radiative decay are predicted to be 1.15(14)×10^{-3} and 4.49(53)×10^{-3}, respectively, which agree well with the experimental measurement data. Our study manifests the potential of lattice QCD studies on the light hadron production in J/ψ radiative decays.