Apotential model for the interaction between a charmed baryon (λc,σc, andσ ∗ c ) and the nucleon (N) is constructed. The model contains a long-range meson (π and σ) exchange part and a short-distance quark exchange part. The quark cluster model is used to evaluate the short-range repulsion and a monopole type form factor is introduced to the long-range potential to reflect the extended structure of hadrons. We determine the cutoff parameters in the form factors by fitting the NN scattering data with the same approach and we obtain four sets of parameters (a)-(d). The most attractive potential (d) leads to bound λcN states with J π = 0+ and 1+ once the channel couplings among λc, σc, and σ∗c are taken into account. One can also investigate many-body problems with the model. Here, we construct an effective λcN one-channel potential with the parameter set (d) and apply it to the three-body λcNN system. The bound states with J = 1/2 and 3/2 are predicted.