A CFD model is created to analyze methanol transport in a flowing electrolyte direct methanol fuel cell (FE‐DMFC) by solving the 3D advection‐diffusion equation, with consideration of electro‐osmosis. The average methanol flux at the anode and cathode surfaces is simulated and compared to equivalent direct methanol fuel cells. Methanol crossover is defined as methanol flux at the cathode surface, and the results reveal that methanol crossover can be drastically reduced by the flowing electrolyte. The performance of the FE‐DMFC at peak power current density is evaluated, and diffusion is shown to be the dominant contribution, although electro‐osmosis increases with current density. The power consumption of the electrolyte pump is shown to be negligible compared to the cell power output. This indicates that thin electrolyte channels with high flow rates could further improve the efficiency.