CERN-LHC. Double-differential three-jet cross-sections have been measured in proton-proton collisions at a centre-of-mass energy of sqrt(s)=7 TeV using the ATLAS detector at the Large Hadron Collider. The measurements are presented as functions of the three-jet invariant mass (m_jjj) and the sum of absolute rapidity separations between the three leading jets (|Y*|). Invariant masses extending up to 5 TeV are reached for 8<|Y*|<10. These measurements use the sample of proton-proton collision data recorded using the ATLAS detector in 2011, which corresponds to an integrated luminosity of 4.51 fb^-1. Jets are identified using the anti-kt algorithm with two different jet radius parameters, R=0.4 and R=0.6. The dominant uncertainty in this measurement comes from the jet energy scale. Next-to-leading-order QCD calculations corrected to account for non-perturbative effects are compared to the measurements. Good agreement is found between the data and the theoretical predictions based on most of the available sets of parton distribution functions, over the full kinematic range, covering almost seven orders of magnitude in the measured cross-section values. The higher precision statistical uncertainties with respect to tables in the paper are represented. 10000 pseudo-experiments were used. In the attachment, there is a tarball containing statistical covariance matrices for data. In the attachment, there is also a tarball containing 10000 pseudo-experiments obtained by fluctuating data in a way described in the reference paper (the bootstrap method). The replicas can be used to study correlations among different ATLAS measurements. In the attachment, there is also a tarball containing tables with non-perturbative corrections.