A high-sensitivity surface plasmon resonance (SPR) sensor is designed and analyzed numerically. The sensor is constructed on the eightfold U-shaped photonic quasi-crystal fiber (PQF) and coated with indium tin oxide (ITO). The coupling between the core mode and surface plasmon polariton mode is enhanced due to shortening of the distance between the core and the ITO layer, so that the PQF-SPR sensor exhibits high refractive index (RI) sensitivity in the near-infrared region. The maximum wavelength sensitivity and the corresponding resolution of this sensor are 42,000 nm/RIU and 2.38×10-6RIU, respectively. The average wavelength sensitivity is 12,750 nm/RIU in the refractive index range of 1.306-1.386. This advanced sensor is suitable for the determination of RIs in the near-infrared region.