We compute the electric dipole moment of nucleons in the large N-c QCD model by Witten, Sakai, and Sugimoto with N-f = 2 degenerate massive flavors. Baryons in the model are instantonic solitons of an effective five-dimensional action describing the whole tower of mesonic fields. We find that the dipole electromagnetic form factor of the nucleons, induced by a finite topological. angle, exhibits complete vector meson dominance. We are able to evaluate the contribution of each vector meson to the final result a small number of modes are relevant to obtain an accurate estimate. Extrapolating the model parameters to real QCD data, the neutron electric dipole moment is evaluated to be d(n) = 1.8 x 10(-16)theta e cm. The electric dipole moment of the proton is exactly the opposite.