The size separation of Brownian particles with the same free mobility in an electrophoretic microchannel with alternating thick regions and narrow constrictions is studied theoretically. The electrophoretic mobility is field dependent and generally increases with field strength. In weak fields, Brownian diffusion dominates and the migration is controlled by the entrance effect. Therefore, smaller particles migrate faster than larger ones. In strong fields, however, the particle tends to follow electric field lines. Smaller particles are susceptible to Brownian motion and thus influenced by the nonuniform electric field in the well significantly. As a result, larger particles possess higher mobilities. Our simulation results agree with the experimental observations and provide guidance for efficient nanofluidic separation.