ABSTRACT Using a density-dependent quark model and a relativistic model within the mean-field approximation for hadrons with density-dependent meson-baryon couplings, we construct, for the first time, models that describe hybrid neutron stars consisting of nucleons and exotic baryons (hyperons and Δ-resonances). We do the study using a Maxwell construction. The quark-hadron phase transition in the stellar matter is determined through the structure, composition, and properties of the hybrid neutron star matter. The macroscopic properties of the star are determined, and the results for these particular models are found to be compatible with recent observational astrophysical data.