Nanoscale quantum plasmon is an important technology that restricts the application of optics, electricity, and graphene photoelectric devices. Establishing a structure-effect relationship between the structure of graphene nanoribbons (GNRs) under stress regulation and the properties of plasmons is a key scientific issue for promoting the application of plasmons in micro-nano photoelectric devices. In this study, zigzag graphene nanoribbon (Z-GNR) and armchair graphene nanoribbon (A-GNR) models of specific widths were constructed, and density functional theory (DFT) was used to study their lattice structure, energy band, absorption spectrum, and plasmon effects under different stresses. The results showed that the Z-GNR band gap decreased with increasing stress, and the A-GNR band gap changed periodically with increasing stress. The plasmon effects of the A-GNRs and Z-GNRs appeared in the visible region, whereas the absorption spectrum showed a redshift trend, indicating the range of the plasmon spectrum also underwent significant changes. This study provides a theoretical basis for the application of graphene nanoribbons in the field of optoelectronics under strain-engineering conditions.