A multi-mode polarization-filtering hollow core anti-resonance fiber whose cladding is composed of four circular tubes and four elliptical tubes is demonstrated. In the vertical directions, two small nested elliptical tubes are coated with gold films in the inner wall. This fiber can filter x-polarized LP01, LP21 and LP02 modes in different wavelengths through surface plasmon resonance which, is produced by two gold films. The polarization extinction ratio of LP01, LP21 and LP02 modes can reach 293, 116 and 30 at the wavelength of 1550 nm, 1570 nm and 1574 nm, respectively. We can adjust the polarization-filtering operation wavelength by changing the ellipticity of elliptical tubes in the cladding. Thus, this fiber can achieve polarization-filtering operation in the whole C and L bands.