Fiducial cross-sections for [Formula: see text] production with one or two additional b-jets are reported, using an integrated luminosity of 20.3 fb[Formula: see text] of proton-proton collisions at a centre-of-mass energy of 8 TeV at the Large Hadron Collider, collected with the ATLAS detector. The cross-section times branching ratio for [Formula: see text] events with at least one additional b-jet is measured to be 950 [Formula: see text] 70 (stat.) [Formula: see text] (syst.) fb in the lepton-plus-jets channel and 50 [Formula: see text] 10 (stat.) [Formula: see text] (syst.) fb in the [Formula: see text] channel. The cross-section times branching ratio for events with at least two additional b-jets is measured to be 19.3 [Formula: see text] 3.5 (stat.) [Formula: see text] 5.7 (syst.) fb in the dilepton channel ([Formula: see text], [Formula: see text], and ee) using a method based on tight selection criteria, and 13.5 [Formula: see text] 3.3 (stat.) [Formula: see text] 3.6 (syst.) fb using a looser selection that allows the background normalisation to be extracted from data. The latter method also measures a value of 1.30 [Formula: see text] 0.33 (stat.) [Formula: see text] 0.28 (syst.)% for the ratio of [Formula: see text] production with two additional b-jets to [Formula: see text] production with any two additional jets. All measurements are in good agreement with recent theory predictions.