Measurements of differential production cross-sections of a Z boson in association with b -jets in pp collisions at √s = 7 TeV are reported. The data analysed correspond to an integrated luminosity of 4.6 fb −1 recorded with the ATLAS detector at the Large Hadron Collider. Particle-level cross-sections are determined for events with a Z boson decaying into an electron or muon pair, and containing b -jets. For events with at least one b -jet, the cross-section is presented as a function of the Z boson transverse momentum and rapidity, together with the inclusive b -jet cross-section as a function of b -jet transverse momentum, rapidity and angular separations between the b -jet and the Z boson. For events with at least two b -jets, the cross-section is determined as a function of the invariant mass and angular separation of the two highest transverse momentum b -jets, and as a function of the Z boson transverse momentum and rapidity. Results are compared to leading-order and next-to-leading-order perturbative QCD calculations.