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.