In this paper, a numerical method to extract rate coefficients of multi-step global reactions for combustion of hydrocarbon fuels with air regarding combustor operating conditions is presented and implemented. The numerical procedure is based on simultaneous interactions of two solvers including a solver for combustive field and another solver as numerical optimizer. A simple reactor solver namely Perfectly Stirred Reactor (PSR) is employed as a solver for reactive flow, and chemical kinetics such as detailed, skeletal or reduced can be considered as benchmark mechanism. Considering rate coefficients of predefined multi-step global reactions as design variables for Differential Evolution (DE) optimizer and the difference between product concentrations obtained from benchmark mechanism and multi-step mechanism as cost function gives optimized values of rate coefficients regarding desired conditions. To confirm reliability and applicability of the present method, three different five-step models is generated for methane-air combustion under three different operating pressure (1.0, 6.28, and 30.0 atm.) and equivalence ratio ranged between 0.4-1.0 for predicting NO and CO emissions. Product concentrations such as NO and CO and flame temperature obtained from the presented five-step mechanisms are closely in agreement with results obtained from the full GRI-3.0 mechanism. A comparative numerical study by means of Computational Fluid Dynamics (CFD) code has been performed for a laboratory scale combustor employing the generated five-step model and an eight-step pressure-dependent global mechanism (suggested by Novosselov) under operating pressure of 6.28 (atm.).