Based on paraxial approximation of beam propagation, intensity and spectra of polychromatic radially polarized beam (PRPB) are investigated during propagation. It is found that, in near field, the increase of the original spectral width introduces a little increase of the beam width of PRPB; however in the far field, the increase of the original spectral width can cause a little decrease of the beam width of PRPB. As to spectral property, there always exists a critical position on observing plane, inside of the critical position, the observed spectrum is blue- shifted, and outside of the critrcal position, the observed spectrum is red- shifted. The increase of original spectral width will push the critical position away from the beam center wherever in the near field or far field. For the case of certain original spectral width, the observed spectral shift width in far field is bigger than that in the near field. Besides, while comparing the PRPB with the polychromatic linearly polarized Gaussian beam, it is found that at the same propagation distance, the radius of the critical position of PRPB is obviously bigger than that of the polychromatic linearly polarized Gaussion beam.