We present a search for standard model Higgs boson production in association with a W boson in proton-antiproton collisions (pp→W±H→ℓνbb) at a center of mass energy of 1.96 TeV. The search employs data collected with the CDF II detector which correspond to an integrated luminosity of approximately 1  fb−1. We select events consistent with a signature of a single lepton (e±/μ±), missing transverse energy, and two jets. Jets corresponding to bottom quarks are identified with a secondary vertex tagging method and a neural network filter technique. The observed number of events and the dijet mass distributions are consistent with the standard model background expectations, and we set 95% confidence level upper limits on the production cross section times branching ratio ranging from 3.9 to 1.3 pb for Higgs boson masses from 110 to 150  GeV/c2, respectively.