Double parton scattering is investigated in proton-proton collisions at = 7 TeV where the final state includes a W boson, which decays into a muon and a neutrino, and two jets. The data sample corresponds to an integrated luminosity of 5 fb(-1), collected with the CMS detector at the LHC. Observables sensitive to double parton scattering are investigated after being corrected for detector effects and selection efficiencies. The fraction of W + 2-jet events due to double parton scattering is measured to be 0.055 +/- 0.002 (stat.) +/- 0.014 (syst.). The effective cross section, sigma (eff), characterizing the effective transverse area of hard partonic interactions in collisions between protons is measured to be 20.7 +/- 0.8(stat.) +/- 6.6(syst.)mb.