The electroosmotic flow induced by an applied potential through microchannels between two parallel plates is analyzed in this study. A 2D Poisson-Boltzmann equation is used to model the electrical double layer (EDL), and the 2D modified Navier-Stokes equation which includes the body force caused by the interaction between the charge density and the applied electrical potential field is also used. These coupled equations are numerically solved with a finite difference method. The detailed results indicate that, in general, the essence of the zeta potential effect on the feature of EOF is significant and clear. The traits of electroosmotic flow with uniform, step change, especially linear variable zeta potential are discussed.