Measurements of differential production cross-sections of a Z boson in association with b-jets in pp collisions at root 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.