The entry flow induced by an applied electrical potential through microchannels between two parallel plates is analyzed in this work. A nonlinear, two-dimensional Poisson equation governing the applied electrical potential and the zeta potential of the solid-liquid boundary and the Nernst-Planck equation governing the ionic concentration distribution are numerically solved using a finite-difference method. The applied electrical potential and zeta potential are unified in the Poisson equation without using linear superposition. A body force caused by the interaction between the charge density and the applied electrical potential field is included in the full Navier-Stokes equations. The effects of the entrance region on the fluid velocity distribution, charge density boundary layer, entrance length, and shear stress are discussed. The entrance length of the electroosmotic flow is longer than that of classical pressure-driven flow. The thickness of the electrical double layer (EDL) in the entry region is thinner than that in the fully developed region. The change of velocity profile is apparent in the entrance region, and the axial velocity profile is no longer flat across the channel height when the Reynolds number is large.