A polarization-independent narrow passband optical filter with a FWHM bandwidth of ~10 MHz based on stimulated Brillouin scattering (SBS) effect is proposed and experimentally demonstrated. By optimizing the parameters of a depolarizer consisting of a power-splitting Mach-Zehnder interferometer (MZI) structure, degree of polarization (DOP) of the pump source can be reduced to less than 5%. Consequently frequency response of the SBS-based filter remains almost unchanged when the state of polarization (SOP) of the input signal varies and the corresponding polarization-dependent gain (PDG) is less than 1 dB. And the experimental results also indicate that the proposed filter can realize the wavelength-independent operation over a range of ~30 nm. Furthermore, high resolution optical spectrum measurement utilizing this novel filter is investigated. For an input signal with a frequency interval of 30 MHz in arbitrary SOP, spectral details can be clearly observed and the power stability of the measured spectra can be improved from 3~5 dB to less than 0.5 dB, which benefitting from the polarization independent operation of the forementioned filter. Moreover, considering the resolution degradation of the measured spectra induced by the frequency shift in the depolarizer, a sweep speed of 5 nm/s for the pump source and a delayed fiber length of 2000 m in the MZI should be used to guarantee the desired high spectral resolution of ~10 MHz.