The gas flow of carbon dioxide from the catalyst layer (CL) through the micro porous layer (MPL) and gas diffusion layer (GDL) has great impacts on the water and fuel management in direct methanol fuel cells (DMFCs). This work has developed a liquid-vapor two-phase model considering the counter flow of carbon dioxide gas, methanol, and water liquid solution in porous electrodes of DMFC. The model simulation includes the capillary pressure as well as the pressure drop due to flow resistance through the fuel cell components. The pressure drop of carbon dioxide flow is found to be about 2-3 orders of magnitude higher than the pressure drop of the liquid flow. The big difference between liquid and gas pressure drops can be explained by two reasons: volume flow rate of gas is three orders of magnitude higher than that of liquid; only a small fraction of pores (< 5%) in hydrophilic fuel cell components are available for gas flow. Model results indicate that the gas pressure and the mass transfer resistance of liquid and gas are more sensitive to the pore size distribution than the thickness of porous components. To build up high gas pressure and high mass transfer resistance of liquid, the MPL and CL should avoid micro cracks during manufacture. Distributions of pore size and wettability of the GDL and MPL have been designed to reduce the methanol crossover and improve fuel efficiency. The model results provide design guidance to obtain superior DMFC performance using highly concentrated methanol solutions or even pure methanol.