A measurement of the cross-section for vector boson production in association with jets containing b-hadrons is presented using 35 pb-1 of data from the LHC collected by the ATLAS experiment in 2010. Such processes are not only important tests of pQCD but also large, irreducible backgrounds to searches such as a low mass Higgs boson decaying to pairs of b-quarks when the Higgs is produced in association with a vector boson. Theoretical predictions of the V+b production rate have large uncertainties and previous measurements have reported discrepancies. Cross-sections measured using in the electron and muon channels will be shown. Comparisons will be made to recent theoretical predictions at the next-to-leading order in αS.