We have investigated a charmed system of DNN (composed of two nucleons and a D meson) by a complementary study with a variational calculation and a Faddeev calculation with fixed-center approximation (Faddeev-FCA). In the present study, we employ a DN potential based on a vector-meson exchange picture in which a resonant A(c)(2595) is dynamically generated as a DN quasi-bound state, similarly to the A(1405) as a (K) over barN one in the strange sector. As a result of the study of variational calculation with an effective DN potential and three kinds of NN potentials, the DNN(J(pi) =0(-), I = 1/2) is found to be a narrow quasi-bound state below A(c)(2595)N threshold: total binding energy similar to 225 MeV and mesonic decay width similar to 25 MeV. On the other hand, the J(pi) =1(-) state is considered to be a scattering state of A(c)(2595) and a nucleon. These results are essentially supported by the Faddeev-FCA calculation. By the analysis of the variational wave function, we have found a unique structure in the DNN(J(pi) = 0, I = 1/2) such that the D meson stays around the center of the total system due to the heaviness of the D meson. (C) 2013 Elsevier B.V. All rights reserved.