Abstract Direct methanol fuel cells (DMFCs) have significant potential to become a leading technology for energy conversion in a variety of applications. However, problems, such as methanol crossover reduce the efficiency and open circuit voltage of the cells. The novel design of flowing electrolyte-direct methanol fuel cells (FE-DMFCs) addresses this issue. Methanol molecules are effectively removed from the membrane electrode assembly (MEA) by the flowing electrolyte, and the unused fuel can be utilized externally. In this paper, a general 3D numerical computational fluid dynamics (CFD) model is established to simulate methanol crossover by convection–diffusion in the FE-DMFC. Illustrations of methanol concentration distribution and methanol molar flux densities are presented, and the performance is compared to conventional DMFCs. The results indicate that methanol crossover can be reduced significantly. A parameter study is performed where the influences of anode fuel feed concentration, electrolyte channel thickness and electrolyte volumetric flow rate on methanol crossover are evaluated. In addition, effects of various electrolyte channel orientations are determined. According to the simulations, counter flow is the superior choice of channel orientations to minimize crossover.