In this study, the dynamic behavior of the performance parameters of an industrial gas turbine used in natural gas compressor stations is modeled using an optimized Nonlinear Autoregressive network with exogenous inputs (NARX). The modeled performance parameters include the turbine fuel flow rate, compressor air mass flow rate, compressor pressure ratio, generator turbine speed, gas temperature at the generator turbine inlet, and exhaust gas temperature at the power turbine outlet. For each target parameter, an independent neural network was developed with two time-varying feedback inputs—namely the turbine speed and the generated power—and two time-invariant external inputs, ambient temperature and installation altitude. To determine the optimal architecture of each network, a grid-search-based approach was employed to obtain the most efficient combination of neurons and delays. The training data for the neural networks were generated using a thermodynamic model of the gas turbine implemented in MATLAB Simulink. To validate the developed models, their simulated outputs were compared with experimental and thermodynamic model results. The obtained correlation coefficients (R) for compressor air flow, fuel flow rate, compressor pressure ratio, generator turbine speed, turbine inlet gas temperature, and turbine exhaust gas temperature were 0.981, 0.994, 0.979, 0.934, 0.987, and 0.968, respectively. Furthermore, comparison of the obtained optimal architectures with a similar previous study demonstrated that the proposed models exhibit lower structural complexity and therefore achieve faster computational performance.