The influence of the electron-phonon (e-ph) interactions on the filed-included polaron dynamics in armchair graphene nanoribbons (GNRs) is theoretically investigated in the scope of a two-dimensional tight-binding model. The results show that the localization of the polaronic charge increases when the strength of e-ph coupling also increases. Consequently, the polaron saturation velocity decreases for higher e-ph coupling strengths. Interestingly, the interplay between the e-ph coupling strength and the GNR width changes substantially the polaron dynamics properties.