This paper details the conceptual design of a thermal–to–14-MeV neutron converter consisting of a mixture of lithium and deuterium in a blanket material. Such a device operates a two-step reaction, first generating tritons via thermal neutron absorption in the tritium breeding material, and in the second step, high-energy neutrons are produced either via deuterium-tritium fusion reaction or with tritium reacting with lithium. A thermal–to–14-MeV neutron converter significantly hardens the neutron spectrum by virtually removing thermal neutrons and adding a high-energy, 14-MeV component to the neutron spectrum. While similar concepts have been previously proposed and tested in other reactors, the unique characteristics of the Advanced Test Reactor (ATR), namely, its important thermal flux (up to n∙cm∙s), make it markedly attractive for obtaining a very large fast neutron flux, usable for irradiation studies under neutron flux conditions prototypical of fusion reactors. The paper provides a description of a new computational scheme developed for handling the coupled neutron-triton transport mechanism using the Geometry and Tracking version 4 (Geant4) toolkit. Resulting neutron spectra and high-energy neutron yields are summarized for different irradiation positions and potential neutron breeder materials. Maximum predicted thermal–to–14-MeV neutron yields are on the order of 2 × 10–4, which is consistent with previous studies found in the literature. Thus, when placed inside the ATR, such a neutron converter will be providing the largest high-energy neutron source available for activation and irradiation studies of materials foreseen for use in fusion reactors. Future steps will involve qualifying the computational scheme using the ATR critical facility using activation foil measurements.