Studying industries energy saving is very important prospect for many researchers in the last four decades. In this respect, better process heat transfer can be achieved to improve process operating and capital cost. Thereafter, obtaining higher amount of heat recovery, which will help to reach system optimum heat exchanger network design. Application of Pinch analysis (PA) in our current study, was found to be as an effective method towards economic solution and assessment for all system thermal processes. Whereby, minimizing energy losses, and thus, prediction of maximum energy saving. In addition, application of "Aspen Energy Analyzer (AEA)" simulation software assist our effort to optimize Heat Exchanger Network design (HEN), with various application scenario towards best design. This study represents a "Case study" as a Brayton closed cycle gas turbine power plant in Al-khairat district, which is one of a number of sites used to generate electricity for Iraq national grid. However, the plant original design is open cycle. This study, represent an attempt to apply (PA) in system closed cycle model with the same working conditions. The results predicted, on the contrary of open cycle, that using closed cycle (PA) with temperature difference ∆Tmin can be acceptable with several design propositions. The optimum (∆Tmin = 15℃) were evaluated in the closed cycle system pinch analysis, thereby the maximum Qrec. process that minimize the QHmin & QCmin requirement were identified by the software simulation for the best HEN design. These results were found as Qrec. = 318.330 MW, QHmin = 88.607 MW and QCmin =39.564 MW.