  A measurement is presented of the cross section for the production of a W
boson with one or two jets, of which at least one must be a b-jet, in pp
collisions at sqrt(s)=7 TeV. Production via top decay is not included in the
signal definition. The measurement is based on 35 pb^-1 of data collected with
the ATLAS detector at the LHC. The W+b-jet cross section is defined for jets
reconstructed with the anti-kt clustering algorithm with transverse momentum
above 25 GeV and rapidity within +/-2.1. The b-jets are identified by
reconstructing secondary vertices. The fiducial cross section is measured both
for the electron and muon decay channel of the W boson and is found to be 10.2
+/- 1.9 (stat) +/- 2.6 (syst) pb for one lepton flavour. The results are
compared with next-to-leading order QCD calculations, which predict a cross
section smaller than, though consistent with, the measured value.
