  The Higgs boson production associated with a $W$-boson and a photon at the
Large Hadron Collider (LHC) can be used to probe the coupling between Higgs
boson and vector gauge bosons and discover a signature of new physics. We
present the precision predictions up to the QCD next-to-leading-order (NLO) in
the standard model for this process involving the subsequential weak decays of
the final Higgs and $W$-boson. The dependence of the leading order (LO) and the
QCD NLO corrected integrated cross sections on the
factorization/renormalization energy scale is studied. We provide the LO and
QCD NLO corrected distributions of the transverse momenta and rapidities of
final products. We find that the LO cross section is significantly enhanced by
the QCD NLO correction, and the $K$-factor value is obviously related to the
physical observables and the phase space regions.
