We present a search for a new heavy charged vector boson W{sup '} 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{sup -1}. No significant excess above the standard model expectation is observed and we set upper limits on {sigma}{center_dot}B(W{sup '}{yields}e{nu}). Assuming standard model couplings to fermions and the neutrino from the W{sup '} boson decay to be light, we exclude a W{sup '} boson with mass less than 1.12 TeV/c{sup 2} at the 95% confidence level.