A measurement of b-hadron pair production is presented, based on a data set corresponding to an integrated luminosity of 11.4 fb(-1) of proton-proton collisions recorded at root s = 8TeV with the ATLAS detector at the LHC. Events are selected in which a b-hadron is reconstructed in a decay channel containing J = psi -> mu mu, and a second b-hadron is reconstructed in a decay channel containing a muon. Results are presented in a fiducial volume de fined by kinematic requirements on three muons based on those used in the analysis. The fiducial cross section is measured to be 17.7 +/- 0.1(stat.) +/- 2.0(syst.) nb. A number of normalised differential cross sections are also measured, and compared to predictions from the PYTHIA8, HERWIG++, MADGRAPH5_AMC@NLO+PYTHIA8 and SHERPA event generators, providing new constraints on heavy flavour production.