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