We report results of a study of the Standard Model Higgs boson discovery potential through the W-pair leptonic decay modes with the ATLAS detector at LHC at 14 TeV center-of-mass energy. We used MC samples with full detector simulation and reconstruction of the ATLAS experiment to estimate the ATLAS detection sensitivity for the reaction of pp -> H -> WW -> e\nu \mu\nu with no hard jet or two hard jets in the final states. The prospects for the Higgs boson searches at ATLAS are presented, including trigger efficiencies and data-driven methods to estimate the backgrounds using control samples in data. With 10/fb of integrated luminosity, one would expect to discover a Standard Model Higgs boson with ATLAS detector in Higgs boson mass range 135 < m_H < 190 GeV. If the Higgs boson does not exist, we will extend and confirm the exclusion produced by the Tevatron Higgs boson search result, which has ruled out the Higgs boson mass range of 160 < m_H < 170 GeV at 95% confidence level. If Higgs boson would be discovered, ATLAS could measure its mass with a precision of about 2 and 7 GeV for Higgs boson mass around 160 GeV and 130 GeV, respectively.