A measurement is presented of the cross-section for b-jet production in association with a Z boson in pp collisions at a centre-of-mass energy of sqrt(s)=7 TeV. The analysis uses the data sample collected by the ATLAS experiment in 2010, corresponding to an integrated luminosity of approximately 36 pb^-1. The event selection requires a Z boson decaying into high pt electrons or muons, and a b-jet, identified by its displaced vertex, with transverse momentum pt>25 GeV and rapidity |y|<2.1. After subtraction of backgrounds, the yield is extracted from the vertex mass distribution of the candidate b-jets. The ratio of this cross-section to the inclusive Z cross-section (the average number of b-jets per Z event) is also measured. Both results are found to be in good agreement with perturbative QCD predictions at next-to-leading order. Show Partial Abstract