Cavity solitons are shape-preserving waveforms infinitely revolving around a cavity, which have numerous applications from spectroscopy to telecommunications. Although the cavity solitons have been widely studied for their special time-frequency characteristics over the past decade, the spectral flatness will be a large limitation in some applications without any extra filtering process. In this paper, we report on the generation of a distinct cavity soliton in a cyclic polarization permutation fiber resonator. With the simultaneous excitation of two orthogonal polarization modes with equally opposite dispersion, vectorial cavity solitons possessing broader and flatter spectra can be generated. In order to verify the concept, a numerical model of the polarization-maintaining fiber is proposed and the soliton with a flattened spectrum can be formed. The results enrich the soliton dynamics in the vectorial dissipation system.