The production cross section of a W boson in association with two b jets is measured using a sample of proton–proton collisions at $\sqrt{s} = 8{,\mathrm{{TeV}}} $ collected by the CMS experiment at the CERN LHC. The data sample corresponds to an integrated luminosity of 19.8 $,\text {fb}^\text {-1}$ . The W bosons are reconstructed via their leptonic decays, $\mathrm {W}\rightarrow \ell \nu $ , where $\ell =\mu $ or $\mathrm {e}$ . The fiducial region studied contains exactly one lepton with transverse momentum $p_{\mathrm {T}} ^{\ell }>30,\mathrm{{GeV}} $ and pseudorapidity $|\eta ^{\ell } |<2.1$ , with exactly two b jets with $p_{\mathrm {T}} >25,\mathrm{{GeV}} $ and $|\eta |<2.4$ and no other jets with $p_{\mathrm {T}} >25,\mathrm{{GeV}} $ and $|\eta |<4.7$ . The cross section is measured to be $\sigma ( {{\mathrm {p}\mathrm {p}}} \rightarrow {\mathrm {W}} (\ell \nu )$ + ${\mathrm{{b}}\mathrm{{\overline{b}}}})= 0.64 \pm 0.03{,\mathrm{{(stat)}}} \pm 0.10{,\mathrm{{(syst)}}} \pm 0.06{,\mathrm{{(theo)}}} \pm 0.02{,\mathrm{{(lumi)}}},{\text {pb}}$ , in agreement with standard model predictions.