In this study, the gas turbine power plant with preheater is modeled and the simulation results are compared with one of the gas turbine power plants in Iran namely Yazd Gas Turbine. Moreover, multiobjective optimization has been performed to find the best design variables. The design parameters of the present study are selected as: air compressor pressure ratio (r(AC)), compressor isentropic efficiency (eta(AC)), gas turbine isentropic efficiency (eta(GT)), combustion chamber inlet temperature (T(3)) and gas turbine inlet temperature. In the optimization approach, the exergetic, economic and environmental aspects have been considered. In multiobjective optimization, the three objective functions, including the gas turbine exergy efficiency, total cost rate of the system production including cost rate of environmental impact and CO(2) emission, have been considered. The thermoenvironomic objective function is minimized while power plant exergy efficiency is maximized using a genetic algorithm. To have a good insight into this study, a sensitivity analysis of the results to the interest rate as well as fuel cost has been performed. In addition, the results showed that at the lower exergetic efficiency in which the weight of thermoenvironomic objective is higher, the sensitivity of the optimal solutions to the fuel cost is much higher than the location of Pareto Frontier with the lower weight of thermoenvironomic objective.