Based on the propagation equation which governs the propagation of ultra-short pulsed beams, and by utilizing the Fourier transform technique as well as the commutation relation between two mathematical operators, the analytical solution for ultra-short pulsed radially polarized beams is obtained. This solution is applicable to radially polarized beams driven by any pulse. On the basis of the solution, the propagation properties of the ultra-short pulsed radially polarized beams are discussed. It shows that the pulse at the beam periphery is delayed compares to that around the beam center. This effect results in the the varying of transverse intensity distribution of the ultra-short pulsed radially polarized beam at different temporal positions during propagation, and the asymmetric intensity distribution of the vertical profle at the head and the trail of the pulse. The method used in this paper is applicable in obtaining the analytical solution and the propagation properties for the ultra-short pulsed azimuthally polarized beams.