  Motivated by the future precision test of the Higgs boson at an $e^+e^-$
Higgs factory, we calculate the production $e^+e^- \to ZH\gamma$ in the
Standard Model with complete next-to-leading order electroweak corrections. We
find that for $\sqrt{s}=240$ (350) GeV the cross section of this production is
sizably reduced by the electroweak corrections, which is $1.03$ (5.32) fb at
leading order and 0.72 (4.79) fb at next-to-leading order. The transverse
momentum distribution of the photon in the final states is also presented.
