The aim of this study is to conduct a parametric investigation of the steam injection gas turbine system by focusing on the effect of the steam mass flow rate on the energy transfer behaviors of a cogeneration plant. A thermodynamic model of two gas turbine cycles and one steam turbine cycle and a heat transfer model of the heat recovery steam generator are developed. A successive iteration is employed to solve a set of equations and obtain a converged solution. The result shows that by increasing the mass flow rate for the steam injection gas turbine system from 0 to 2 kg/s, the input energy rate from the fuel and the total electrical output power from the cogeneration plant are increased, resulting in an increase of the cogeneration electrical efficiency from 49.9% to 50.4%. On the other hand, the output heat rate from the steam from the cogeneration plant is decreased, resulting in a decrease of the cogeneration heat efficiency from 8.5% to 5.4%. Consequently, the primary energy saving of the cogeneration plant decreases from 16.6% to 14.9%.