With the advent of nanotechnology, nano-electro-osmosis flow (nano-EOF) has shown great promise in the next generation of lab-on-a-chip systems such as attoliter or picoliter syringes or pipettors. In order to optimize the design of such systems and to precisely control analysis processes, it is important to obtain better fundamental understanding of EOF at nanoscales. Therefore, a more comprehensive electric double layer (EDL) theory is in need to improve upon the conventional EDL theory based on the Poisson-Boltzmann (PB) equation. In this paper, the modified PB theory is utilized to investigate the flow behavior of EOF at micro- and nanoscales. The effect of ion size and the image effect are particularly emphasized. Both effects remarkably influence nano-EOF. More importantly, this study predicts a new phenomenon: two "peaks" may appear in the velocity profile of nano-EOF for some specific solid-electrolyte systems.