Abstract Using angle-resolved photoemission spectroscopy and density functional theory calculations methods, we investigate the electronic structures and topological properties of ternary tellurides NbIrTe$_{4}$, a candidate for type-II Weyl semimetal. We demonstrate the presence of several Fermi arcs connecting their corresponding Weyl points on both termination surfaces of a topological material. Our analysis reveals the existence of Dirac points, in addition to Weyl points, giving both theoretical and experimental evidence of the coexistence of Dirac and Weyl points in a single material. These findings not only confirm NbIrTe$_{4}$ as a unique topological semimetal but also open avenues for exploring novel electronic devices based on its coexisting Dirac and Weyl fermions.