  We investigate the QCD next-to-leading order (NLO) corrections to the
production of a pair of fermionic dark matter particles associated with a W
boson production through a mediator which couples to standard model particles
via either a vector or axial-vector coupling at the LHC. We find that the QCD
NLO corrections reduce the dependence of the total cross sections on the
factorization and renormalization scales, and the $K$-factors increase with the
increment of the dark matter mass. We also provide the LO and QCD NLO corrected
distributions of the transverse momenta $p_T^\mu$ of final muon and transverse
mass $M_T$. We find that the LO cross section is significantly changed by the
QCD NLO corrections.
