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We calculate the annihilation decay widths of spin-singlet heavy quarkonia$h_c, h_b$ and $\eta_b$} into light hadrons with both QCD and relativisticcorrections at order $O(\alpha_{s}v^{2})$ in nonrelativistic QCD. Withappropriate estimates for the long-distance matrix elements by using thepotential model and operator evolution method, we find that our predictions ofthese decay widths are consistent with recent experimental measurements. Wealso find that the $O(\alpha_{s}v^{2})$ corrections are small for $b\bar{b}$states but substantial for $c\bar{c}$ states. In particular, the negativecontribution of $O(\alpha_{s}v^{2})$ correction to the $h_{c}$ decay can lowerthe decay width, as compared with previous predictions without the$O(\alpha_{s}v^{2})$ correction, and thus result in a good agreement with therecent BESIII measurement.

QCD and Relativistic $O(\alpha_{s}v^2)$ Corrections to Hadronic Decays of Spin-Singlet Heavy Quarkonia $h_c, h_b$ and $\eta_b$