  Cross sections of the heavy quarkonium production process $e^+e^-\to H +
\gamma$ at the c.m. energy of $Z^0$-boson resonance are calculated at leading
order in $\alpha_s$ with relativistic corrections resummed within the framework
of nonrelativistic QCD (NRQCD). $S$- and $P$-wave charmonia and bottomonia are
considered. For $J/\psi(\Upsilon)$ production, the result of
vector-meson-dominance (VMD) approach is also given. Relativistic contributions
to charmonium production are of the same magnitude as next-to-leading order QCD
corrections, decreasing cross section 20-30%. Relativistic corrections to
bottomonium production are negligible, not exceeding 2%.
