In this paper, we propose a high-performance graphene-dielectric metasurface that is applied as an optical biosensor. The proposed metasurface is based on an array of asymmetric grooved silicon disks grown over a graphene sheet. The asymmetric silicon disks lead to the formation of a high quality factor (Q-factor) Fano resonance. In addition to the sharp resonance, the strong field confinement provided by annular grooves results in an enhanced light-analyte interaction and sensitivity of as high as 640 nm/RIU. According to the presented results, the biosensor exhibits a high linearity R2 value of 0.999 and low resolution of 1.56e-4 RIU. Furthermore, the proposed biosensor is polarization-insensitive with a figure of merit (FOM) as high as 784 RIU−1. To the best of our knowledge, this is the highest FOM ever reported for a polarization-insensitive biosensor. Such characteristics are promising for effective detection of biomolecules like hemoglobin. Finally, the effect of surface roughness on performance of the proposed biosensor is investigated where different resonance characteristics and sensitivities are obtained. It implies that the proposed structure as a multiparameter sensor could be applied for biosensing and also for evaluation of the amount of surface roughness due to fabrication errors.