  In this paper, we investigate the decay of Higgs boson to $J/\psi(\Upsilon)$
plus a photon based on NRQCD factorization. For the direct process, we
calculate the decay width up to QCD NLO. We find that the decay width for
process $H \to J/\psi(\Upsilon)+ \gamma$ direct production at the LO is
significantly reduced by the NLO QCD corrections. For the indirect process, we
calculate the $H \to \gamma^\ast\gamma$ with virtual $\gamma$ substantially
decaying to $J/\psi(\Upsilon)$, including all the SM Feynman diagrams. The
decay width of indirect production is much larger than the direct decay width.
Since it is very clean in experiment, the $H \to J/\psi(\Upsilon)+ \gamma$
decay could be observable at a 14 TeV LHC and it also offers a new way to probe
the Yukawa coupling and New Physics at the LHC.
