The channel H -> gamma gamma is the most promising in which to discover a light Higgs boson with ATLAS at LHC. The ATLAS detector is one of the four experiments at the Large Hadron Collider at CERN and will, according to current planning, become operational in 2007. This thesis describes an analysis of the channel done with fast simulation of the signal and background processes in the mass range 120 - 150 GeV. The significance of the signal is calculated with the standard counting experiment technique and also with a more advanced statistical procedure. The concept of splitting the events into two channels where the signal resolution is different is also introduced.