A two-core hollow optical fiber for a polarizer based on surface plasmon resonance (SPR) is proposed and studied by the full-vector finite-element method. The proposed fiber consists of two circular cores, inner cladding, outer cladding, and a large central air hole. The two cores are arranged symmetrically in inner cladding and couple weakly with the air hole. There is no cross talk between cores because they are insulated by the air hole. A nanodimension Ag/Au bimetallic layer can be coated on the inner surface of the central air hole to support SPR. The numerical results show that single polarization of two cores is achieved simultaneously at the wavelength of 1.310 μm, due to strong coupling between the TM mode and the surface plasmon polariton mode. The extinction ratio 40.90 dB with 3 mm length is obtained, and the confinement loss of TE mode is 0.19 dB/cm. Moreover, the resonance wavelength is tunable by varying the refractive index of materials in the central air hole. The scheme is helpful for coupling an all-fiber polarizer with multicore polarization maintaining fibres (PMFs) and makes possible application in in-fiber integrated interferometric sensors while maintaining polarization.