Electroosmotic flow (EOF) pumps find applications in precise control of fluids in microchannels. EOF pumps are known to generate flowrates and pressures. They can easily be fabricated using microfabrication techniques. Based on the reported efficiency of electroosmotic flow, this work presents simulation-based study of electroosmotic micropump which can readily be integrated with other Microelectromechanical systems (MEMS) components for drug delivery. In this work, three structures of miniaturised microchannels are designed and simulated. These channels utilise the electroosmotic effects predominant near the sidewalls of the channel where microelectrodes are mounted. Pumping process is initiated by applying low voltage potential to the microelectrodes. Finite-Element-Method (FEM) simulation is used for the laminar flow studies in the microchannels with the application of 10–30 V. Net average velocities for different geometric structures are obtained by applying variable voltages to the electrodes. For a single channel pump, a very low backpressure (only 1 Pa) is achieved which cannot be useful for pumping typically for transdermal drug delivery. Hence, electroosmotic micropump consisting of multiple narrow channel micropump and cascaded channel micropump structure are used. Parallel channel micropump gives flow velocity of 750 µm/s (at 30 V) and 0.8 kPa backpressure, cascaded channel micropump gives 125.83 µm/s (at 30 V) and 1.6 kPa for 10 stages and 125.83 µm/s (at 30 V) and 2.4 kPa for 15 stages. Hence, in cascaded structure, one can notice a significant increase in backpressure after increasing the number of stages. But stages cannot be increased to very large extent due to increasing in complexity.