The electrokinetic flow of an electrolyte solution through an elliptical microchannel is studied theoretically. The system under consideration simulates the flow of a fluid, for example, in vein. We show that, for a constant cross-sectional area, both the electroosmotic volumetric flow rate and the streaming potential increase monotonically with an increase in the aspect ratio, and both the total electric current and the electroviscous effect may exhibit a local minimum as the aspect ratio varies. Also, for a constant average potential on the channel wall, the difference between the results based on three kinds of boundary conditions, which include constant surface charge, constant surface potential, and charge-regulated surface, is inappreciable if the hydraulic diameter is larger than 1 mum.