Energy and exergy analyses are reported for a modified oxy-fuel cycle, which includes the Graz cycle with an atmospheric condensation and a dual-pressure heat recovery steam generator (HRSG). Oxy-fuel cycles are proposed to capture all the produced CO2. Due to limited fossil fuel resources, it is necessary to optimise the use of energy in the power plant cycles as much as possible. The presented configuration improves the energy and exergy efficiency of the cycle with usage of dual-pressure HRSG instead of single pressure. In this study, thermodynamic analysis for the performance of modified Graz cycle has been done which shows the effect of different parameters on the performance of cycle. Results show that the thermal and exergy efficiencies increase up to 54.5% and 47.8%, respectively, by adding of dual-pressure heat recovery steam generator unit.