Recent developments in Micro Electro Mechanical Systems (MEMS) related areas have increased the demand for practical and novel pumping methods. How to drive fluid is a hard question because of high pressure drop in micro scale. Different methods has been suggested to solve this problem, among which, electroosmotic pump is preferred because of its advantages. Utilizing electroosmotic force for flow generation in microchannels has become popular recently, because of its reliable operation and control. One of the potential applications of MEMS is biological and medical analysis. The cross section of such devices are often close to rectangular shape. Also the application of alternative current in microfluidic has created many interest. In this study, hydrodynamic characteristics of Newtonian fluids under combined unsteady electroosmotic and pressure driven flow in rectangular microchannel is analyzed. It is assumed that the flow is fully developed and a pressure gradient would also affect the fluid flow inside the channel. In most related studies, different simplified assumptions are made in order to obtain analytical solutions such as the assumption of Debye-Huckel linearization. But in this study the electrical potential distribution in the channel is obtained directly by numerical solution of the non-linear Poisson–Boltzmann equation without the Debye–Huckel approximation. The non dimensional governing equations along with the Poisson–Boltzmann equation are solved using the Fluent software. The body force due to the electrical field is included in the momentum equation. Both Poisson–Boltzmann equation and the body force are added to the software as the user define functions. Parametric studies show that as the electric field frequency increases, the perturbed flow region becomes smaller and the flow at the channel center remains virtually motionless. This phenomenon is logically anticipated because as the frequency becomes very high, the electric field changes its direction so fast that the flow cannot response fast enough to develop across the entire channel. Changing the size of the channel affects both the Electric Double Layer (EDL) and the velocity profile, moreover, it is demonstrated a noticeable ‘‘corner effect’’. The results reveal that the effect of presence of small favorable pressure gradient is seen at the channel center whereas the alternative electrical field affects the flow near the wall. By increasing the zeta potential, the maximum velocity is increased. Even though increasing both the ion concentration and electric field cause higher body force, the electric field has higher efficiently than the concentration. It is because increasing the concentration is accompanied by decrease of the EDL thickness. Finally, the results are compared with the available analytic and numerical solutions and it is shown that the approximation of the Poisson–Boltzmann equation such as Debye-Huckel approximation results in significant errors specially near the wall Keywords: Microfluidics, Electroosmotic flow, Debye-Huckel, Pressure gradient