Graphene holds great promise in the field of nanoelectronic devices owing to its high carrier mobility, excellent overall electrical properties, and good mechanical performance. Theoretically, the Dirac cone band structure of intrinsic graphene endows it with unique electrical properties. However, the utility of standalone graphene layers is limited by factors such as a lack of self-support and high environmental sensitivity in practical applications. In recent years, hexagonal boron nitride (h-BN), a two-dimensional material structurally analogous to graphene, has been introduced as an ideal material for fabricating heterostructures, which not only provides mechanical support and environmental protection for graphene but also modulates its band structures and electronic transport properties, thereby expanding its technological application prospects. This paper constructs three distinct stacking configurations of graphene/hexagonal boron nitride (h-BN) heterostructures and investigates their structural, electronic, and piezoresistive properties. The three stacking configurations along the c-axis are characterized as follows: carbon atoms aligned with both nitrogen and boron atoms (G-BN1), nitrogen atoms centered within the carbon hexagonal rings (G-BN2), and boron atoms centered within the hexagonal rings (G-BN3). Structural optimization of the heterostructures was performed based on the generalized gradient approximation (GGA) and density functional theory (DFT). Interlayer binding energy calculations reveal that G-BN2 exhibits the lowest binding energy, indicating relatively stronger interlayer interactions between graphene and h-BN in this stacking configuration. The band structures and density of states (DOS) of the three stacking configurations were calculated using the Heyd–Scuseria–Ernzerhof (HSE06) hybrid functional. The results indicate that the introduction of h-BN modulates the π-electron band structure of graphene, thereby inducing bandgap opening. In-plane uniaxial and biaxial tensile strains induced by external stress were simulated by increasing the lattice constants along the a-axis and along both the a- and b-axes, respectively. The band structure variations and piezoresistive properties of the three stacking configurations under these strain conditions were calculated. Compared to the unstrained structures, the bandgaps of all stacking heterostructures significantly increase under uniaxial strain but narrow under biaxial strain; additionally, graphene/h-BN heterostructures effectively enhance piezoresistive coefficient of graphene, and the anisotropic response of electronic orbitals leads to higher piezoresistive coefficients for all configurations under uniaxial strain. Among them, the G-BN2 stacking configuration exhibits the highest piezoresistive coefficient under both strain conditions. This study establishes a theoretical foundation for the future design of graphene-based piezoresistive devices.