This paper proposes a recent approach-based moth-flame optimizer (MFO) to enhance the output power of solid oxide fuel cell (SOFC) via identifying the optimal parameters of its model. The cell is modeled via artificial neural network (ANN) trained by experimental dataset. Six inputs are fed to ANN to get the SOFC terminal voltage. Levenberg-Marquardt is used in training process with minimizing the mean squared error (MSE). The SOFC model polarization curves are compared to experimental data under variable operating conditions. The proposed MFO is employed to estimate the optimal values of SOFC model, anode support layer (ASL) thickness; ASL porosity; thickness of electrolyte and cathode functional layer (CFL) thickness to enhance the SOFC extracted power. Furthermore, a quantitative and qualitative comparative study with ANN-based SOFC optimized via Genetic Algorithm (GA), Social Spider Optimizer (SSO), Radial Movement Optimizer (RMO) and the experimental data is presented under different operating conditions. Sensitivity analysis is performed by changing the upper and lower thresholds of the estimated variables. The proposed ANN-MFO approach enhanced the SOFC power by 18.92% and 5.56% in comparison with ANN-GA and ANN-RMO respectively. The obtained results confirmed the significance of the proposed MFO in enhancing of the SOFC output power.