The overall performance of heavy-duty gas turbines is strongly affected by the mass flow distribution of the secondary air system. Reducing the mass flow of the secondary air is a remarkable method to improve the performance of a gas turbine. The aim of this article is to implement a brush seal as an alternative to labyrinth seal. Based on the experiences gained from the integrity of brush seals into a gas turbine, installing a brush seal would not necessarily improve turbine performance. This is because of SAS mass flow redistribution, which may not lead to overall SAS mass flow reduction. Therefore, some other components in the SAS arrangement should be modified as controlling variables to overcome this problem. The effect of these modifications on the airflow distribution is investigated using an in-house network analysis code. To establish an optimum solution (optimized brush seal geometry and controlling variables), the network analysis code is coupled with an in-house optimization code that benefits from the Genetic Algorithms and Artificial Neural Networks. Some constraints including upstream and downstream cavity purge flow and vane cooling air are considered in the optimization process. The final network results show a 33.27% reduction in overall SAS mass flow. To ensure an improvement in the performance of the new three-stage turbine, a CFD analysis is conducted, which indicates 1.0% more power with respect to the original turbine. In the end, the aerodynamic and mechanical behavior of the brush seal is analyzed using CFD and FEM.