The production of W bosons in association with two jets in proton-proton collisions at a centre-of-mass energy of root s = 7 TeV has been analysed for the presence of double-parton interactions using data corresponding to an integrated luminosity of 36 pb(-1), collected with the ATLAS detector at the Large Hadron Collider. The fraction of events arising from double-parton interactions, f(DP)((D)), has been measured through the p(T) balance between the two jets and amounts to f(DP)((D)) = 0.08 +/- 0.01 (stat.) +/- 0.02 (sys.) for jets with transverse momentum p(T) > 20 GeV and rapidity vertical bar y vertical bar < 2.8. This corresponds to a measurement of the effective area parameter for hard double-parton interactions of sigma(eff) = 15 +/- 3 (stat.)(-3)(+5) (sys.) mb.