An analytical study of the effect of diffusioosmosis caused by the concentration gradient of hydrogen ions on the isothermal transport of water in a fully hydrated membrane of a polymer electrolyte fuel cell (PEFC) is presented. A capillary tube or slit with a negatively charged wall is chosen to model the nanopores of the membrane. The electric double layer adjacent to the capillary wall may have an arbitrary thickness relative to the capillary radius and its electrostatic potential distribution is determined as the solution of the Poisson–Boltzmann equation. Solving a modified Navier–Stokes equation, the fluid velocity in the axial direction of the capillary induced by the macroscopic electric field and protonic concentration gradient is obtained as a function of the radial position in closed forms. The results for the local and averaged electrokinetic velocities in the capillary show that the effect of diffusioosmosis on the water transport in the membrane of a PEFC can be significant in comparison with that of electroosmosis under low-potential-difference operations.