By using the first-principles method based on the density-functional theory, twisting- deformation-dependent electrical characteristics of graphene nanoribbons (GNRs) are studied systematically. It is shown that the energy gap of the zigzag-edge graphene nanoribbon (ZGNR) is the most insensitive to twisting deformation, and it almost keeps metallicity unchanged, next is the armchair-edge graphene nanoribbons (AGNRs) by width W=3p-1 (p is a positive integer), and its gap has only a small change when twisting deformation occurs. However, the gap of AGNR with width W=3p+1 is extremely sensitive to twisting deformation, and it can display a variation from wide-gap semiconductor to moderate-gap semiconductor, quasi-metal, and metal, next is AGNR with W=3p. In other words, the larger the band gap for GNR in the absence of twisting deformation, the more significant the change (becoming small) of its band gap with twisting deformation. Additionally, for the whole electronic structure and transmission behavior, one can find that there is a much larger influence under twisting deformation in AGNR than in ZGNR. These studies suggest that it is necessary to take the effect of twisting deformation on the electrical characteristics into account in designing GNR-based nanodevices.