We present a hybrid graphene/dielectric metasurface design to achieve strong tunable and modulated transmission at near-infrared (near-IR) frequencies. The proposed device is constituted by periodic pairs of asymmetric silicon nanobars placed over a silica substrate. An one-atom-thick graphene sheet is positioned over the all-dielectric metasurface. The in-plane electromagnetic fields are highly localized and enhanced with this metasurface due to its very low Ohmic losses at near-IR wavelengths. They strongly interact with graphene. Sharp Fano-type transmission spectrum is obtained at the resonant frequency of this hybrid configuration due to the cancelation of the electric and magnetic dipole responses at this frequency point. The properties of the graphene monolayer flake can be adjusted by tuning its Fermi energy or chemical potential, leading to different doping levels and, equivalently, material parameters. As a result, the Q-factor and the Fano-type resonant transmission spectrum of the proposed hybrid system can be efficiently tuned and controlled due to the strong light-graphene interaction. Higher than 60% modulation in the transmission coefficient is reported at near-IR frequencies. The proposed hybrid graphene/dielectric nanodevice has compact footprint, fast speed, and can be easily integrated to the current CMOS technology. These features would have promising applications to near-IR tunable filters, faster optical interconnects, efficient sensors, switches, and amplitude modulators.