We experimentally demonstrated polarization multiplexing schemes in a tilted fiber grating (TFBG) to achieve polarization-independent fiber-optic surface plasmon resonance (SPR) sensors. The first used two orthogonal polarized lights separated by a polarization beam splitter (PBS) that are p-polarized in polarization-maintaining fiber (PMF) and precisely aligned with the tilted grating plane, so as to achieve the transmission of p-polarized light in two opposite directions of the Au-coated TFBG to excite SPR. Alternatively, polarization multiplexing was also achieved by exploring two polarization components to achieve the SPR effect through a Faraday rotator mirror (FRM). The SPR reflection spectra are polarization-independent of the light source and any perturbations to fibers, which are explained by the superposition of p- and s-polarized transmission spectra in equal proportions. The spectrum optimization is presented to reduce the proportion of the s-polarization component. A polarization-independent TFBG-based SPR refractive index (RI) sensor with a wavelength sensitivity of 555.14 nm/RIU and an amplitude sensitivity of 1724.92 dB/RIU for small changes is obtained, exhibiting unique advantages of minimizing the polarization alterations by mechanical perturbations.