The binding energies ∈_η and widths Г_η of η-mesic nuclei are calculated. We parameterize the η self-energy in the nuclear medium as a function of energy and density. We find that the single-particle energies are sensitive to the scattering length, and increase monotonically with the nucleus. The key point for the study of η-nuclens bound states is the η-nuclear optical potential. We study the s-wave interactions of η mesons in a nuclear medium and obtain the optical potential U_η ≈ -72 MeV. Comparing our results with the previous results, we find that the TIN scattering length a_(ηN) is indeed important to the calculations. With increasing nuclear density the effective mass of the η meson decreases.