A mathematical model is an important tool for analysis and design of fuel cell stacks and systems. In general, the complete description of fuel cells requires an electrochemical model to predict their electrical characteristics, i.e., cell voltage and current density. However, obtaining the electrochemical model is quite a difficult and complicated task as it involves various operational, structural and electrochemical reaction parameters. In this study, a neural network model was first proposed to predict the electrochemical characteristics of solid oxide fuel cell (SOFC). Various NN structures were trained based on the back-propagation feed-forward approach. The results showed that the NN with optimal structure reliably provides a good estimation of fuel cell electrical characteristics. Then, a neural network hybrid model of a direct internal reforming SOFC, combining mass conservation equations with the NN model, was developed to determine the distributions of gaseous components in fuel and air channels of SOFC as well as the performance of the SOFC in terms of power density and fuel cell efficiency. The effects of various key parameters, e.g., temperature, pressure, steam to carbon ratio, degree of pre-reforming, and inlet fuel flow rate on the SOFC performance under steady-state and isothermal conditions were also investigated. A combination of the first principle model and NN presents a significant advantage of predicting the SOFC performance with accuracy and less computational time. Copyright (C) 2011, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights reserved.