Aiming at overpressure measurement, this paper presents a large-range graphene/hexagonal boron nitride (h-BN) heterostructure-based pressure sensor with a poly(methyl methacrylate) (PMMA) substrate. Graphene and h-BN are chosen as sensitive materials because they both have large Young’s modulus, high intrinsic strength, high natural frequency, and atomic thickness at the same time. These characteristics provide favorable conditions for the application of the sensor in the high pressure and high frequency dynamic environment. Moreover, the photoresist-assisted transfer technology is proposed for transferring graphene from the growth substrate to the PMMA substrate and the lift-off method with exposure and development is developed to achieve metal patterning on the PMMA substrate. The sensor characterization results suggest that the graphene and h-BN films have good transfer qualities and the heterojunction possesses excellent electrical performance. The static pressure loading experiments confirm that the sensor has a pressure range of up to 85 MPa and its piezoresistive coefficient is 0.7 GPa−1, which indicates that the designed sensor is suitable for overpressure fields. This study provides a novel method for determining overpressure and lays a foundation for the fabrication of graphene-based electronic devices with an organic substrate.