  Since the precise study of Higgs gauge couplings is important to test the
Standard Model (SM), we calculate the complete next-to-leading order QCD(NLO
QCD) correction to the $pp \to HZW^{\pm}$ production in the SM at 14 TeV LHC.
Our results show that the NLO QCD correction can enhance the leading-order
cross section of $pp \to HZW^{\pm}$ by 45%, when $ m_H $ = 125.3 GeV. We also
study the dependence of the LO and NLO corrected cross sections on the
renormalization and factorization scale $\mu$. Besides, due to the unbalance of
parton distribution functions, we investigate the charge asymmetry of $W^{\pm}$
in the production of $pp\to HZW^{\pm}$, which can reach 32.94% for
$\mu=(m_H+m_Z+m_W)/2$ at 14 TeV LHC.
