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We investigated edge configuration and quantum confinement effects on electron transport in armchair-edged graphene nanoribbons (A-GNRs) by using a computational approach. We found that the edge bond relaxation has a significant influence not only on the bandgap energy but also on the electron effective mass. We also found that A-GNRs with N = 3m family (N is the number of atoms in its transverse direction, and m is a positive integer) exhibits smaller effective mass by comparing it at the same bandgap energy. As a result, A-GNRs with N = 3m family are found to be favorable for use in channels of field-effect transistors.