  The associated production of Higgs boson with a hard photon at lepton
collider, i.e., $e^+e^-\to H\gamma$, is known to bear a rather small cross
section in Standard Model, and can serve as a sensitive probe for the potential
new physics signals. Similar to the loop-induced Higgs decay channels $H\to
\gamma\gamma, Z\gamma$, the $e^+e^-\to H\gamma$ process also starts at one-loop
order provided that the tiny electron mass is neglected. In this work, we
calculate the next-to-leading-order (NLO) QCD corrections to this associated
$H+\gamma$ production process, which mainly stem from the gluonic dressing to
the top quark loop. The QCD corrections are found to be rather modest at lower
center-of-mass energy range ($\sqrt{s}<300$ GeV), thus of negligible impact on
Higgs factory such as CEPC. Nevertheless, when the energy is boosted to the ILC
energy range ($\sqrt{s}\approx 400$ GeV), QCD corrections may enhance the
leading-order cross section by $20\%$. In any event, the $e^+e^-\to H\gamma$
process has a maximal production rate $\sigma_{\rm max}\approx 0.08$ fb around
$\sqrt{s}= 250$ GeV, thus CEPC turns out to be the best place to look for this
rare Higgs production process. In the high energy limit, the effect of NLO QCD
corrections become completely negligible, which can be simply attributed to the
different asymptotic scaling behaviors of the LO and NLO cross sections, where
the former exhibits a milder decrement $\propto 1/s$ , but the latter undergoes
a much faster decrease $\propto 1/s^2$.
