Graphene has good mechanical properties including large Young's modulus, making it ideal for many resonant sensing applications. Nonetheless, the development of graphene-based sensors has been limited due to difficulties in fabrication, encapsulation, and packaging. Here, we report a graphene nanoresonator-based resonant pressure sensor. The graphene nano resonator is fabricated on a thin silicon diaphragm that deforms due to pressure differential across it. The deformation-induced strain change results in a resonance frequency shift of the graphene nano resonator. The pressure sensing experiments demonstrate a record high responsivity of 20 kHz/kPa over a range of 270 kPa. The design has the potential to reach responsivities up to 500 kHz/kPa. The reported responsivity is two orders of magnitude higher than the silicon-based resonant pressure sensors. The estimated resolution of pressure sensing is 90 Pa, which is 0.03% of the full-scale range of the pressure sensor. This exceptional performance is attributed to two factors: maintaining a high-quality vacuum environment for the nanoresonator and introducing stimuli through a thin silicon diaphragm. The proposed pressure sensor design provides flexibility to adjust responsivity, range and footprint as needed. The fabrication method is simple and has the potential to be integrated into the modern semiconductor foundries.