The neutron-drip-line nucleus 23 N is investigated in a three-body model consisting of a 21 N core and two valence neutrons. Using the Faddeev formalism with the realistic neutron-neutron potential and the neutron-core potential, we calculate the ground-state properties of 23 N including its twoneutron separation energy, and obtain good agreement with the experiments. We also find an excited 23 N state with a shallow two-neutron separation energy at about 0.18 MeV. By evaluating the root-mean-square matter radii, the average distances between the two valence neutrons, and the average distances from the core to the center-of-mass of the valence-neutron pair, we show that the excited state of 23 N has a distinct halo structure. Through calculating the correlation density distributions of the 23 N three-body system in configuration space, we find that the excited state of 23 N has a triangular shape, which is similar to but much more extended than the ground state.This scaling symmetry between the ground and excited states indicate the existence of an Efimov state in 23 N.