Fiducial cross-sections for tt¯ production with one or two additional b-jets are reported, using an integrated luminosity of 20.3 fb-1 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 tt¯ events with at least one additional b-jet is measured to be 950 ± 70 (stat.) -190+240 (syst.) fb in the lepton-plus-jets channel and 50 ± 10 (stat.) -10+15 (syst.) fb in the eμ channel. The cross-section times branching ratio for events with at least two additional b-jets is measured to be 19.3 ± 3.5 (stat.) ± 5.7 (syst.) fb in the dilepton channel (eμ, μμ, and ee) using a method based on tight selection criteria, and 13.5 ± 3.3 (stat.) ± 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 ± 0.33 (stat.) ± 0.28 (syst.)% for the ratio of tt¯ production with two additional b-jets to tt¯ production with any two additional jets. All measurements are in good agreement with recent theory predictions.