This thesis presents a measurement of the production cross-section of a Z boson in association with at least one or two b-jets. This final state occurs in the Standard Model and can be used to test predictions from perturbative quantum chromodynamics. It is also an important background for several processes including Higgs production, with the Higgs decaying to a b-quark pair, in association with a vector boson as well as searches for physics beyond the Standard Model which contain leptons and b-jets in the final state. The measurement is done using data collected by the ATLAS detector from proton-proton collisions at a center-of-mass energy of 13 TeV at the LHC corresponding to an integrated luminosity of 35.6 fb^-1. The integrated and differential cross-sections are measured at the particle level for both the electron and muon decay channels of the Z boson. The results are compared to predictions from several Monte Carlo predictions.