Pumps with step microelectrodes subjected to an ac voltage are known to have faster pumping rates than those with planar asymmetric microelectrodes. The driving force for pumping in these systems is ac electro-osmosis. This paper aims to understand the flow behaviors of pumps with step microelectrodes by using a realistic model applicable to high external voltages. This model takes the steric effect due to the finite sizes of ions into account and copes with the exponential sensitivity of the counterion concentration to voltage. The effects on the pumping flow rate of varying the pump parameters were investigated. The geometrical parameters were optimized, and the effects of varying the ac frequency and amplitude were examined. The electrical potential of the fluid and the electrical charge at the electrode surface were solved simultaneously, and the Stokes equation was used to describe the fluid flow.