The energy band structure, the transmission spectrum and the current-voltage characteristics of the N-doped zigzag graphene nanoribbons (z-GNRs) have been investigated by performing first-principles calculations. The results show the appearance of energy gap and a metal-semiconductor transition induced by N-doping of z-GNRs. With impurity concentration increasing, the current under the same bias decreases significantly, while the transmission coefficient near the Fermi surface decreases gradually. In addition, the length, the width and the N-doping position of z-GNR affect the transport property. Especially, the impurity concentration competes with the N-doping position in the influence on the transport property for narrow z-GNRs.