Here, we propose a polarization-independent wavelength-tunable first-order fiber comb filter based on a polarization-diversified loop configuration. The proposed filter is composed of a polarization beam splitter, two equal-length high birefringence fiber (HBF) segments, three half-wave retarders (HWRs), and two quarter-wave retarders (QWRs). Among these five wave retarders (WRs), a group of an HWR and a QWR is located in front of each HBF. The third remaining HWR is positioned after the second HBF segment and utilized to adjust the effective orientation angle of this HBF. On the basis of the filter transmittance derived through Jones formulation, orientation angle sets of the five WRs, which can induce an arbitrary phase shift from 0 to 2π in the transmittance function, are found at both flat-top and narrow band transmission spectra. From theoretical transmission spectra obtained at eight selected orientation angle sets of the five WRs, which cause phase shifts increasing linearly from 0 to 7π/4 by a step of π/4, it is confirmed that the flat-top or narrow band comb spectrum can be continuously tuned by properly controlling the WR orientation angles. Then, this theoretical prediction is verified by experimental demonstration. In particular, the spectral evolution of the output states of polarization (SOPs) of the third HWR, the last one of optical components contained within the polarization-diversified loop, is investigated on the Poincare sphere. The relationship of the passband shape and wavelength tuning with the spectral evolution of the SOP is also discussed.