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We investigate the transport properties of bilayer AA-stacking zigzag graphene nanoribbons (bi-zGNRs) and observe abnormal I-V characteristics which are sensitive to the number of carbon chains across the ribbons. Combining the chirality selective rule of Dirac electrons in graphene and the symmetry of eigenstates, we attribute the abnormal current behavior to the chirality mismatch of energy states. The mismatch causes the suppression of transmission pathways between two electrodes which lead to saturated current with increasing bias for certain ribbons.