Nonlinear electro-osmotic behaviour of dilute non-adsorbing polymer solutions with low salinity is investigated using Brownian dynamics simulations and a kinetic theory. In the Brownian simulations, the hydrodynamic interaction between the polymers and a no-slip wall is considered using the Rotne-Prager approximation of the Blake tensor. In a plug flow under a sufficiently strong applied electric field, the polymer migrates toward the bulk, forming a depletion layer thicker than the equilibrium one. Consequently, the electro-osmotic mobility increases nonlinearly with increasing electric field and becomes saturated. This nonlinear mobility does not depend qualitatively on the details of the rheological properties of the polymer solution. Analytical calculations using the kinetic theory for the same system quantitatively reproduce the results of the Brownian dynamics simulation well.