In this paper, we propose a scotogenic model of neutrino masses with flavor-dependent $U(1)_{B-3L_\alpha}(\alpha=e, \mu, \tau)$ gauge symmetry, in which neutrinos are generated at one-loop level and a fermion dark matter is naturally accommodated. In this model, three one-zero-texture structures of neutrino mass matrix, denoted as patterns A, B and C, are successfully realized by appropriate charge assignment for inert fermions and scalar fields. For each predicted textures, a detailed numerical analysis is carried out to find the allowed regions of neutrino mixing and masses. We find three scenarios (A for normal mass hierarchy, and B and C for inverted mass hierarchy) favored by the latest data of neutrino oscillation experiments and Planck 2018 limit on the sum of neutrino masses. Other phenomenologies such as lepton flavor violation, dark matter and collider signatures are also discussed.