In cases of the microfluidic channel, where the thickness of electric double layer is often comparable with the characteristic size of flow channels, the electrokinetic influence on the flow behavior can be found. The externally applied body force originating from the electrostatic interaction between the linearized Poisson-Boltzmann field and the flow-induced electrical field is applied in the equation of motion. An analytical solution to this Navier-Stokes equation of motion for well-defined geometry of slit-like microchannel is obtained by employing Green’s function. Also, an explicit analytical expression for the induced electrokinetic potential is successfully derived as functions of relevant physicochemical parameters. The effects of the ionic concentration of the fluid, the zeta potential of the solid surface, and the width of microchannels on the velocity profile as well as the streaming potential are examined. The electric double layer effect on the velocity profile becomes stronger as the channel width decreases, where the average fluid velocity is entirely reduced with the decrease in ionic concentration. The induced electrokinetic potential increases with an increase in pressure gradient, while it decreases as the ionic concentration increases.