Transmission, conductivity, and shot noise are investigated in multi-barrier resonant tunneling structures based on the pseudospin-1 Dirac–Weyl model. Super Klein tunneling, perfect transmission plateau, and resonant tunneling collectively contribute to the transport properties. While resonant tunneling occurs when the energy of the passing quasiparticle coincides with the discrete quasibound energy level of the multi-barrier structure and is widely observed in parabolic and Dirac-cone-shape dispersive materials, super Klein tunneling and perfect transmission plateau are unique in pseudospin-1 systems and barrier-structure independent. As a result, the conductivity and shot noise in pseudospin-1 resonant-tunneling multi-barrier structures demonstrate remarkably different properties from their counterparts of both parabolic-dispersion semiconductors and pseudospin-1/2 Dirac–Weyl materials, typically graphene. It is found that the zero conductivity minimum remains for multi-barrier structures and the relative shot noise indicated by the Fano factor in the three-barrier system is larger than that in the double-barrier system when the Klein tunneling effect weakens.