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The exotic structures of the ground state of the mirror nuclei 17Ne and 17N are investigated by means of the asymptotic normalization coefficient (ANC) method to explore the role of the Coulomb interaction. The probabilities of a valence nucleon outside the binding-potential are P = 56.69±2.987.46%for 17Ne and P = 45.51 ±2.325.81% for 17N. The rms radii are 1/2 5.06±0.110.30 fm and 1/2 = 4.24±0.060.16 fm, respectively. The results obtained are nearly independent of the potential parameters. According to the halo occurrence conditions, it is suggested that 17 Ne is a two-proton halo and 17 N is a two-neutron skin. Moreover, two effects of the Coulomb interaction on the exotic structure are analysed. From the present results, the exotic structure of the nucleus in the proton-rich side is more obvious than that of its mirror nucleus because of the Coulomb interaction.