A three-dimensional, two-phase model is developed to study a direct methanol fuel cell (DMFC). In the proposed model anode and cathode flow channels, gas diffusion layers, catalyst layers and membrane are considered. An in-house CFD code (on the basis of SIMPLE algorithm) is used to solve the governing equations which include conservations of mass, momentum, energy, and species as well as electrochemical kinetics in the fuel cell. The cell is simulated continuously through different layers. Thus, satisfying the boundary conditions only at the walls, and the anode and cathode flow channel inlet and outlet are required. A smooth and orthogonal grid with appropriate stretches is generated to enhance the accuracy of the results at high gradient areas. Several case studies are conducted to examine DMFC performance at different pressures and temperatures. The results indicate that the cell power density is improved at elevated pressures and temperatures. However, one should bear in mind that system reliability (which is a great concern for portable applications) may suffer as a result of rise in these parameters.