In proton exchange membrane fuel cells (PEMFCs), the permeability of the gas diffusion layer (GDL) differs between the in-plane and through plane directions, and the overall permeability in the shoulder region is typically lower than that in the channel region due to the clamping force applied through the bipolar plates. Here, we conducted a numerical investigation of GDLs with different isotropic or anisotropic permeabilities in the channel and shoulder regions for PEMFCs. A three-dimensional, non-isothermal model was employed with a single straight channel. We found that the water and thermal management in PEMFCs depend on the permeability characteristics of the GDL, especially in the shoulder region. Moreover, the ohmic loss and cathode overpotential varied depending on the difference in isotropic permeability between the channel and shoulder regions. In the study on GDLs with anisotropic permeabilities in the channel and shoulder regions, however, we found that variations in the anisotropic permeabilities in the channel and shoulder regions, had little effect on the cathode overpotential at the shoulder region, but caused significant changes in ohmic loss as the ohmic loss depended on water and thermal management. In addition, we found that the cell temperature was much higher in GDLs with low anisotropic permeabilities due to hindering of the water removal process.