To meet the needs for neutron capture therapy (NCT) irradiations, a high-intensity, high-quality fission converter-based epithermal neutron beam has been designed for the MITR-II research reactor. This epithermal neutron beam, capable of delivering treatments in a few minutes with negligible background contamination from fast neutrons and photons, will be installed in the present thermal column and hohlraum of the 5-MW MITR-II research reactor. Spent or fresh MITR-II fuel elements will be used to fuel the converter. With a fission converter power of ~80 kW using spent fuel, epithermal fluxes (1 eV < E < 10 keV) in excess of 1010 n/cm2s are achievable at the target position with negligible photon and fast neutron contamination, i.e., <2 × 10-11 cGycm2/n. With the currently available 10B delivery compound boronophenylalanine-fructose, average therapeutic ratios of ~5 can be achieved using this beam for brain irradiations with deep effective penetration (~9.5 cm) and high dose rates of up to 400 to 600 RBE cGy/min. If NCT becomes an accepted therapy, fission converter-based beams constructed at existing reactors could meet a large fraction of the projected requirements for intense, low-background epithermal neutron beams at a relatively low cost. The results of an extensive set of neutronic design studies investigating all components of the beam are presented. These detailed studies can be useful as guidance for others who may wish to use the fission converter approach to develop epithermal beams for NCT.