Double-differential three-jet production cross-sections are measured in proton-proton collisions at a centre-of-mass energy of root s = 7 TeV using the ATLAS detector at the large hadron collider. The measurements are presented as a function of the three-jet mass (m(jjj)), in bins of the sum of the 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 a sample of 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-k(t) algorithm with two different jet radius parameters, R = 0.4 and R = 0.6. The dominant uncertainty in these measurements 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.