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-1, collected with the ATLAS detector at the Large Hadron Collider. The fraction of events arising from double-parton interactions, f(D) DP, has been measured through the pT balance between the two jets and amounts to f(D) DP = 0.08 ±0.01 (stat.)±0.02 (sys.) for jets with transverse momentum pT > 20 GeV and rapidity |y| < 2.8. This corresponds to a measurement of the effective area parameter for hard double-parton interactions of σeff = 15 ± 3 (stat.) +5 -3 (sys.) mb.