The importance of reducing water crossover from anode to cathode in a direct methanol fuel cell (DMFC) has been well documented, especially if highly concentrated methanol fuel is to be used. A low-α membrane electrode assembly (MEA) with thin membrane is key to achieving this goal. The low water crossover from anode to cathode for these types of MEAs has traditionally been attributed to the use of a hydrophobic cathode micro-porous layer (MPL). However, it has recently been discovered that a hydrophobic anode MPL also reduces the water crossover, possibly even more significantly than a hydrophobic cathode MPL. In this work, we develop and use a 1D, two-phase transport model that accounts for capillary-induced liquid flow in porous media to explain how a hydrophobic anode MPL controls the water crossover from anode to cathode. We further show that a lower water crossover can lead to a lower methanol crossover via dilution of methanol in the anode catalyst layer. Finally, we perform a parametric study and show that a thicker anode MPL with greater hydrophobicity and lower permeability is more effective in reducing the water crossover.