CERN-LHC. Measurements of the inclusive and dijet production cross sections for jets containing b-hadrons from proton-proton collisions at a centre-of-mass energy of 7 TeV. The analysis uses a data sample with total integrated luminosity of 34 pb^{-1}. b-jets are identified using either a lifetime-based method using vertex information or a muon-based method using the presence of a muon to identify semileptonic decays. The inclusive cross section is measured as a function of PT in range 20 to 400 GeV with |y| < 2.1. The dijet cross section is measured as a function dijet invariant mass in the range 100 to 760 GeV, the azimuthal difference between the two jets and the angular variable chi (defined as exp|y1-y2|) in two dijet mass regions. Note added (27 JUN 2014): The cross section values reported in Tables 1-7 below should be multiplied by a factor of 1.0187 to take into account the updated value of the integrated luminosity for the ATLAS 2010 data taking period. The uncertainty on the global normalisation ("Lumi") increases slightly from 3.4% to 3.5%. See Eur.Phys.J. C73 (2013) 2518 for more details.