A novel method based on a cat-eye cavity laser and a Mach-Zehnder interferometer is presented to generate various axially symmetric linearly-polarized vector beams (ASLPVB) by modes superposition. Transverse modes of TEM00, TEM01, TEM10, TEM11, TEM20, TEM21, TEM30 and TEM31 are obtained by adjusting the cat-eye cavity laser. And then, four kinds of ASLPVB, whose polarization orders and initial azimuthal polarization angles are (+1，0°), (+1，-90°), (-1，0°) and (-1,90°) respectively, are further achieved by modes superposition using the Mach-Zehnder interferometer. The transmitted intensities of generated beams passing through a linear polarizer are further measured using a CCD, which verify the polarization properties of generated vector beams. Various forms of ASLPVB can also be generated using such method in one system, which does not need special optical components, costs least and operates easily.