In twisted h-BN/graphene heterostructures, the complex electronic properties of the fast-traveling electron gas in graphene are usually considered to be fully revealed. However, the randomly twisted heterostructures may also have unexpected transition behaviors, which may influence the device performance. Here, we study the twist-angle-dependent coupling effects of h-BN/graphene heterostructures using monochromatic electron energy loss spectroscopy. We find that the moiré potentials alter the band structure of graphene, resulting in a redshift of the intralayer transition at the M point, which becomes more pronounced up to 0.22 eV with increasing twist angle. Furthermore, the twisting of the Brillouin zone of h-BN relative to the graphene M point leads to tunable vertical transition energies in the range of 5.1-5.6 eV. Our findings indicate that twist-coupling effects of van der Waals heterostructures should be carefully considered in device fabrications, and the continuously tunable interband transitions through the twist angle can serve as a new degree of freedom to design optoelectrical devices.