This paper reports a measurement of the W +b-jets (W +b+ X and W + bb¯ +X) production cross-section in proton-proton collisions at a centre-of-mass energy of 7 TeV at the LHC. These results are based on data corresponding to an integrated luminosity of 4.6 fb−1, collected with the ATLAS detector. Cross-sections are presented as a function of jet multiplicity and of the transverse momentum of the leading b-jet for both the muon and electron decay modes of the W boson. The W +b-jets cross-section, corrected for all known detector effects, is quoted in a limited kinematic range. Combining the muon and electron channels, the fiducial cross-section for W +b-jets is measured to be 7.1 ± 0.5 (stat) ± 1.4 (syst) pb, consistent with the next-to-leading order QCD prediction, corrected for non-perturbative and double-parton interactions (DPI) contributions, of 4.70 ± 0.09 (stat) +0.60−0.49 (scale) ±0.06 (PDF) ±0.16 (non-pert) +0.52−0.38 (DPI) pb.