Graphene nanoribbons (GNRs) are important nanomaterials. A carbon nanotube can be viewed as a GNR rolled into a seamless cylinder. By using the first-principles method based on the density-functional theory, the rolling deformation-dependent electronic characteristics of GNRs, including the band structure (particularly the bandgap), density of states (DOS), and transmission spectrum, are studied systematically. It is found that before all types of GNRs are rolled into carbon nanotubes, they are not sensitive to the rolling deformations, which means that for electronic structures and transport properties, GNRs have a very strong ability to resist the rolling deformations. After GNRs are rolled into nanotubes, zigzag-edge GNRs (ZGNRs) and armchair-edge GNRs (AGNRs) present distinct differences in property, ZGNRs almost maintain unchanged metallic behaviors or become quasi-metallic. But for AGNRs, their electronic characteristics experience large variations, and transformations occur between the quasi-metal and semiconductor with various bandgaps, which might be closely related to the periodical boundary conduction along the direction of tubular circumference of a carbon nanotube and variation of quantum confinement. These studies presented here are of significance for understanding the rolling effects on electronic characteristic and relationship of electronic characteristics between GNRs and carbon nanotubes (structure-property relationship).