We present the results of a search for the Standard Model Higgs boson in its associated production with a W vector boson in pp collisions at [special characters omitted] = 1.96 TeV using the complete Run IIA dataset with an integrated luminosity of 1.04 fb^-1 collected by the DØ experiment. The salient features of this analysis are the extended geometric acceptance by including the pseudorapidity covered by the end cap calorimeter, optimization in b-tagging and event selection criteria. We observe very good agreement in the data compared to the expectation form the modeling of Standard Model background for the WH signal. No excess events in data are observed over the predicted background. We establish that the evidence for observing the Higgs boson in this channel is inconclusive and proceed to set upper cross section limits on the associated WH production at 95% confidence level. We derive the cross section upper limits for the Higgs mass (m_H) ranging from 105 GeV/c² to 145 GeV/c². For m _H = 115 GeV/c², the observed (expected) upper limit is 0.8 (0.9) pb compared to the Standard Model expectation of 0.13 pb.