We propose a surface plasmon resonance (SPR) sensor based on a single mode optical fiber with six air holes. A thin gold film and a TiO2 film are deposited on the walls of air holes. Due to high refractive index of TiO2 the proposed sensor can operate at near-infrared (IR) wavelengths. The characteristics of the sensor were numerically investigated based on the finite-element method (FEM). The numerical results indicate that the optical loss spectrum of SPR sensor can be tuned easily by changing the thicknesses of gold and TiO2 layers. The refractive-index resolution of 2.7×10−5 (sensitivity S≈370/RIU) for aqueous analytes can be achieved.