Fiducial cross-sections for tˉt production with one or two additional b-jets are presented, 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 tˉt events with at least one additional b-jet is measured to be 950 ± 70 (stat.) +240−190 (syst.) fb in the lepton-plus-jets channel and 50 ± 10 (stat.) +15−10 (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, 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 tˉt production with two additional b-jets to tˉt production with any two additional jets. NB: When merging several output YODA files, the ratio (d02-x01-y01) needs to be reconstructed in a post-processing step.