In the published studies, to the best of the authors’ understanding, the grey Taguchi-based statistical technique has not been applied for the optimization of combined gas-steam power plants. In view of this, seven essential input parameters namely compressor inlet air temperature, pressure ratio, fuel temperature, volumetric flow rate of fuel, gas turbine maximum temperature, compressor efficiency, and turbine efficiency are chosen with the aim of determining the optimal combination of design variables that maximize the net power generation, thermal efficiency, exergetic effciency, and minimize the specific fuel consumption. Also, the impact weight of each parameter on output indicators has been evaluated. While the Taguchi approach helps to create an orthogonal array of L27 (3^7), the ANOVA method determines the contribution of each input argument on the objective function. Unlike the Taguchi and ANOVA optimization methodology, the grey relational analysis is performed to transform the multi-objective function into a single objective by way of estimating its grey relational grade. The most favorable combination of input parameters is determined as A1B1C1D1E3F3G3 and under this state, the optimum values of power generation, thermal efficiency, exergetic efficiency, and specific fuel consumption are found to be 259911 kW, 64.9 %, 66.27 %, and 0.1839 kg/kWh respectively. Moreover, the contribution ratio on the output characteristic of the combined cycle is found to be maximum for turbine efficiency (42.41 %) and minimum for fuel temperature (0.59 %). The effectiveness of the grey-Taguchi method is acknowledged and validated using an artificial neural network technique in MATLAB.