This paper reports a numerical study on the steady state developing electro-osmotic flow in closed-end cylindrical micro-channels. To simulate the flow, a mathematical model, which includes the Poisson-Boltzmann equation describing the electrical distribution and the modified two-dimensional Navier-Stokes equations governing the velocity field, is presented. The governing equations are discretized using the control volume integration method, and the staggered grid system is utilized to solve the Navier-Stokes equations. The results of the spatial development of the flow field and the pressure distributions along the micro-channel are presented. Parametric studies of the effects of the channel size and electric field strength on electro-osmotic flows in closed-end micro-channels are conducted. It is found that the length of the developing region is only dependent on the radius of the channel, and the induced backpressure gradient, though is present in the entire channel, varies only in the developing region. In addition, the numerical simulations have been validated with the analytical solutions in the fully developed region.