Graphene plasmons have tremendous potential applications in middle-infrared to terahertz frequencies. Previous studies mainly focused on the coupling between graphene plasmon and phonon of substrate, while the approach to modulate such coupling has been rarely reported. One possible approach to modulate such coupling is to change the dielectric environment around graphene nanoribbons (GNRs). Numerical simulation indicates that compared with GNRs on flat SiO2 substrate, GNRs in grooves demonstrate stronger coupling between plasmon and phonon. In addition, the dispersion curve of plasmons shifts down when the frequency is away from the frequency of phonon, and the maximum absorption of the two dispersion curve branches at low frequency is also significantly improved. On the contrary, GNRs on the SiO2 protruding platform lead to contrary results. Such observations reveal that the coupling between graphene plasmon and phonon of substrate can be efficiently modulated by simply changing the edge dielectric environment of GNRs.