The electro-osmosis through an annulus is investigated. The electric potential and flow velocity profile are obtained by solving the linearized Poisson-Boltzmann equation and the Stokes equation. Both the thin and thick double layer limits are analyzed. Under the condition of thin double layer, the electro-osmotic mobility can be described by the Helmholtz-Smoluchowski equation with a geometry-dependent correction factor. There exist net flows even for zero area-averaged surface charge density due to the curvature differences between the inner and outer walls. The flow direction is determined by the sign of the charge on the inner cylinder. We also found that under certain circumstances the flow direction in an annulus is opposite to that in a capillary with the same sign of the net charge.