The production of W bosons in association with two jets in proton-proton collisions at a centre-of-mass energy of sqrt(s)=7 TeV has been analysed for the presence of double-parton interactions using data corresponding to an integrated luminosity of 36/pb, collected with the ATLAS detector at the LHC. The fraction of events arising from double-parton interactions, fDP(D) has been measured through the momentum balance between the two jets and amounts to fDP(D) = 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 \sigma_eff = 15 +- 3 (stat.) +5 -3 (sys.) mb.