The inclusive and dijet production cross-sections have been measured for jets containing b-hadrons (b-jets) in proton--proton collisions at a centre-of-mass energy of √s=7 TeV, using the ATLAS detector at the LHC. The measurements use data corresponding to an integrated luminosity of 34 pb−1. The b-jets are identified using either a lifetime-based method, where secondary decay vertices of b-hadrons in jets are reconstructed using information from the tracking detectors, or a muon-based method where the presence of a muon is used to identify semileptonic decays of b-hadrons inside jets. The inclusive b-jet cross-section is measured as a function of transverse momentum in the range 20<pT<400 GeV and rapidity in the range |y|<2.1. The bˉb-dijet cross-section is measured as a function of the dijet invariant mass in the range 110<m_{jj}<760 GeV, the azimuthal angle difference between the two jets and the angular variable χ in two dijet mass regions. The results are compared with next-to-leading-order QCD predictions. Good agreement is observed between the measured cross-sections and the predictions obtained using POWHEG+Pythia6. MC@NLO+Herwig shows good agreement with the measured bˉb-dijet cross-section. However, it does not reproduce the measured inclusive cross-section well, particularly for central b-jets with large transverse momenta.