This paper describes a measurement of the W boson transverse momentum distribution using ATLAS pp collision data from the 2010 run of the LHC at sqrt(s) = 7 TeV, corresponding to an integrated luminosity of about 31 pb^-1. Events from both W -> e nu and W -> mu nu are used, and the transverse momentum of the W candidates is measured through the energy deposition in the calorimeter from the recoil of the W. The resulting distributions are unfolded to obtain the normalized differential cross sections as a function of the W boson transverse momentum. We present results for pTW < 300 GeV in the electron and muon channels as well as for their combination, and compare the combined results to the predictions of perturbative QCD and a selection of event generators.