We present a search for a new heavy charged vector boson W′ decaying to an electron-neutrino pair in pp collisions at a center-of-mass energy of 1.96 TeV. The data were collected with the CDF II detector and correspond to an integrated luminosity of 5.3  fb−1. No significant excess above the standard model expectation is observed and we set upper limits on σ⋅B(W′→eν). Assuming standard model couplings to fermions and the neutrino from the W′ boson decay to be light, we exclude a W′ boson with mass less than 1.12  TeV/c2 at the 95% confidence level.