In this research, the performance and kinetics of an iron/manganese oxide catalyst in a fixed-bed reactor by Fischer-Tropsch Synthesis is studied. The range of operating conditions are; P = 1 – 12 bar, T = 513 - 553 K, H2/CO ratio = 1 - 2 and GHSV = 4200 – 7000 ((〖cm〗^3 (STP))/h/g_cat). The effect of these independent variables, on Fischer-Tropsch product were performed by using a statistical model based on experimental data. Two models, response surface methodology and artificial neural network, were applied for modeling and predicting of the experimental points for carbon monoxide conversion (CO% conversion) and catalytic kinetic for the consumption rate of CO (-rco). Some statistical parameters such as correlation coefficient and mean square error were calculated to capability and sensitivity analysis of two models. Results show that two models, have good agreement with experimental data but artificial neural network model was stronger and more accurate than the response surface method model. To achieve the optimum condition, optimization must be done. It was obtained that maximum amount of CO% conversion was achieved in P = 8 bar, T = 559.5 K, H2/CO = 2.5 and GHSV = 7325.2 ((〖cm〗^3 (STP))/h/g_cat) and maximum amount of consumption rate of CO was in P = 8 bar, T= 568 K, H2/CO = 2.5 and GHSV = 2800 ((〖cm〗^3 (STP))/h/g_cat). Finally, all of quadratic equations and optimum conditions for any variable and responses will be concluded.