Inclusive four-jet events produced in proton-proton collisions at a centre-of mass energy of root s = 7 TeV are analysed for the presence of hard double-parton scattering using data corresponding to an integrated luminosity of 37.3 pb(-1), collected with the ATLAS detector at the LHC. The contribution of hard double-parton scattering to the production of four -jet events is extracted using an artificial neural network, assuming that hard double-parton scattering can be approximated by an uncorrelated overlaying of dijet events. For events containing at least four jets with transverse momentum PT >= 20 GeV and pseudorapidity vertical bar eta vertical bar <= 4.4, and at least one having pT >= 42.5 GeV, the contribution of hard double-parton scattering is estimated to be fDps = 0.092(-0.011)(+0.0005) (stat.) (+0.03337)(-0.011) (syst.). After combining this measurement with those of the inclusive dijet and four -jet cross -sections in the appropriate phase space regions, the effective cross-section, sigma(eff,) was determined to be sigma(eff) = 14.9(-1.0)(+1.2) (stat.) (+5.1)(-3.8) (syst.) mb. This result is consistent within the quoted uncertainties with previous measurements of sigma(eff), performed at centre-of-mass energies between 63 GeV and 8 TeV using various final states, and it corresponds to 21(-6%)(+7) of the total inelastic cross-section measured at root s = 7 TeV. The distributions of the observables sensitive to the contribution of hard double-parton scattering, corrected for detector effects, are also provided.