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 √s=7  TeV, corresponding to an integrated luminosity of about 31  pb^-1. Events form both W→eν and W→μν 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 p_T^W<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.