A method for generating a high-order (≥2 ) polarized vortex beam by using achromatic meniscus axicon doublets (MADs) is described. The MAD has a rotationally symmetric structure and consists of a pair of identical meniscus axicons with the same apex angle. It exploits four total internal reflections when collimated rays pass through it to produce a half-wave retardation, but with azimuth-variant polarization orientations. The characteristics of high achromatism of retardance, reasonable acceptance angular aperture for MAD, are numerically demonstrated. The effect of the remaining stress birefringence of optical materials on retardation is also discussed.