We proposed a surface plasmon resonance (SPR) refractive index sensor based on hollow-core anti-resonance fiber (HC-ARF). Gold was filled in two symmetric cladding tubes of the fiber, while the analyte was filled in central air holes. The sensing performance was investigated by the finite element method (FEM). Results show that two resonance peaks (a crossing point around 1 030 nm and an anti-crossing region around 1 065 nm) appear for x-polarization (x-pol) core mode coupling with the surface plasmon polariton (SPP) mode. Moreover, the sensitivity was also analyzed. The sensitivity increased with the increase of cladding tube thickness t. The sensor with thickness t=1.7 μm gave a wavelength sensitivity of 7 350—14 790 nm/RIU in the refractive index range of 1.33—1.45 with resonance wavelength from 1 900 nm to 450 nm. Meanwhile, the resolution of 10-6 RIU was achieved. Thanks to high sensitivity and resolution, the proposed sensor has potential applications in glucose detection.