New, neutral gauge bosons appear in various theories extending beyond the current theory of particle physics, the Standard Model. In this thesis we review the discovery potential of one specific gauge boson, the Sequential Standard Model Z', with the ATLAS detector at LHC. A feasibility study is performed at 10 TeV center of mass collisions, ultimately ending in the discovery reach as a function of the Z' mass. The full 2010 data taken at 7 TeV center of mass energy, corresponding to ~40 pb-1, are analysed first with focus on the Z0 boson resonance and the performance of the ATLAS detector with leptons. This is then followed by a search for high mass resonances decaying to electron-positron pairs and muon-antimuon pairs. Based on statistical errors only, the SSM Z' with mass up to 995 GeV is excluded at 95% confidence level.