We report a graphene-based indium tin oxide coated surface plasmon resonance sensor built on a D-shaped optical fiber for near infrared. Different parameters of the proposed sensor have been optimized to obtain a maximal phase matching between the core guided mode and the plasmon mode using finite element method. Wavelength sensitivity of the proposed structure is as high as 5700 nm/RIU with a maximum resolution of 1.754 × 10-5 RIU. The proposed sensor can also be used for bio layer thickness monitoring with a maximum resolution of 62.5 pm in wavelength interrogation. © 2015 IEEE.