Free electrons moving in an optical standing wave field feel the ponderomotive potential, acting as a refractive-index medium in electron optics. Emerging technologies involving this potential have been proposed and realized in electron microscopy, such as electron phase-contrast imaging using a laser standing wave in an optical enhancement cavity. However, the interaction between electrons and a cylindrically distributed optical field has not been investigated despite its suitability for electron-optical imaging systems. In this study, we theoretically show that the divergence and convergence forces are provided by tightly focused cylindrically polarized light beams. The radially and azimuthally polarized beams with an annular profile are focused using a high-numerical-aperture optical lens. The intensity distributions at the focus function are concave and convex electron round lenses, respectively. The convex lens formed by the azimuthally polarized beam possesses negative (opposite sign) spherical aberration compared with conventional electron round lenses created by electrodes and magnetic coils. This remarkable result will contribute to the innovative design of electron-optical imaging systems and advances in matter-wave optics.