The effect of some operating conditions such as temperature, gas hourly space velocity (GHSV), CH4/O2 ratio and diluents gas (mol% N2) on ethylene production by oxidative coupling of methane (OCM) in a fixed bed reactor at atmospheric pressure was studied over Mn/Na2WO4/SiO2 catalyst. Based on the properties of neural networks, an artificial neural network was used for model developing from experimental data. To prevent network complexity and effective data input to the network, principal component analysis method was used and the number of output parameters was reduced from 4 to 2. A feed-forward back-propagation network was used for simulating the relations between process operating conditions and those aspects of catalytic performance including conversion of methane, C2 products selectivity, C2 yielding and C2H4/C2H6 ratio. Levenberg-Marquardt method is presented to train the network. For the first output, an optimum network with 4-9-1 topology and for the second output, an optimum network with 4-6-1 topology was prepared. After simulating the process as well as using ANNs, the operating conditions were optimized and a genetic algorithm based on maximum yield of C2 was used. The average error in comparing the experimental and simulated values for methane conversion, C2 products selectivity, yield of C2 and C2H4/C2H6 ratio, was estimated as 2.73%, 10.66%, 5.48% and 10.28%, respectively.