A measurement is presented of the inclusive cross-section for b-jet production in association with a Z boson in pp collisions at a centre-of-mass energy of √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 pTpT electrons or muons, and at least one b-jet, identified by its displaced vertex, with transverse momentum pT>25 GeVpT>25 GeV and rapidity |y|<2.1|y|<2.1. After subtraction of background processes, 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.