  The $W$-pair production in association with a massive (anti)bottom jet is not
only an important background to a number of interesting processes, such as the
single top production associated with a W boson, but also a potential
background to new physics searches. We present the calculations of the total
and differential cross sections for the $W^+W^-+ b(\bar{b})$ jet productions at
the LHC up to the QCD next-to-leading order (NLO). Our results by adopting the
QCD NLO contribution collection scheme-I show that the K factors can be 1.66
and 1.21 with the inclusive and exclusive two-jet event selection schemes
respectively, when we set $m_H=120 GeV$, $\mu=m_W+m_b/2$ and take the
constraints of $p_{T,b(\bar{b})}>25 GeV$, $|y_{b(\bar{b})}|<2.5$ for
$b(\bar{b})$ jet. We find that the stabilization of the theoretical prediction
for the integrated cross section for the $pp \to W^+W^-b(\bar b)+X$ up to the
QCD NLO requires a veto on a second isolated hard jet and the inclusion of the
QCD NLO contribution from the $W^+W^-b\bar{b}(bb, \bar{b}\bar{b})$ production
with the final two $b(\bar{b})$ quarks being merged as one jet.
