In this paper a numerical model is,developed for a novel reactor combining a Solid Oxide Electrolyzer Cell (SOEC) section with a Fischer Tropsch like section for methane production under pressurized & temperature-gradient condition. Governing equations for mass, momentum, charge transport are solved with Finite Element Method. The chemical reaction kinetics of reversible water gas shift reaction and reversible methanation reaction in Ni/YSZ cathode are fully considered. The model is validated by comparing simulation results with experimental data. Parametric simulations are conducted to understand the physical-chemical processes in the reactor with a focus on the pressure effect. It is predicted that the optimal operating pressure is around 3 bar, beyond which the CH4 conversion ratio (2.5 times enhanced than 1 bar operating) cannot be further increased. It is also found that it is feasible to operate the pressurized SOEC at a lower temperature for CH4 production with improved catalyst activity. (C) 2016 Elsevier Ltd. All rights reserved.