This paper presents a measurement of the production cross-section of aZboson in association withb-jets, in proton-proton collisions at root s = 13 TeV with the ATLAS experiment at the Large Hadron Collider using data corresponding to an integrated luminosity of 35.6 fb(-1). Inclusive and differential cross-sections are measured for events containing aZboson decaying into electrons or muons and produced in association with at least one or at least two b-jets with transverse momentum p(T)>20 GeV and rapidity vertical bar y vertical bar <2.5. Predictions from several Monte Carlo generators based on leading-order (LO) or next-to-leading-order (NLO) matrix elements interfaced with a parton-shower simulation and testing different flavour schemes for the choice of initial-state partons are compared with measured cross-sections. The 5-flavour number scheme predictions at NLO accuracy agree better with data than 4-flavour number scheme ones. The 4-flavour number scheme predictions underestimate data in events with at least one b-jet.