Amplifying radially and azimuthally polarized beams is a significant challenge due to the instability of the complex beam shape and polarization in inhomogeneous environment. In this Letter, we demonstrated experimentally an efficient approach to directly amplify cylindrical-vector beams with axially symmetric polarization and doughnut-shaped intensity profile in a picosecond MOPA system based on a double-clad ytterbium-doped tapered fiber. To prevent polarization and beam shape distortion during amplification, for the first time to the best of our knowledge, we proposed using the spun architecture of the tapered fiber. In contrast to an isotropic fiber architecture, a spun configuration possessing nearly circular polarization eigenstates supports stable wavefront propagation. Applying this technique, we amplified the cylindrical-vector beam with 10 ps pulses up to 22 W of the average power at a central wavelength of 1030 nm and a repetition rate of 15 MHz, maintaining both mode and polarization stability.