A design for a slab reactor to produce an epithermal neutron beam and a thermal neutron beam for use in neutron capture therapy (NCT) is described. A thin reactor with two large-area faces, a “slab” reactor, was planned using eighty-six 20% enriched TRIGA fuel elements (General Atomics, San Diego, California) and four B4C control rods. Two neutron beams were designed: an epithermal neutron beam from one face and a thermal neutron beam from the other. The planned facility, based on this slab-reactor core with a maximum operating power of 300 kW, will provide an epithermal neutron beam of 1.8 × 109 nepi/cm2·s intensity with low contamination by fast neutrons (2.6 × 10−13Gy· cm2/nepi) and gamma rays (<1.0 × 10−13 Gy·cm2/nepi) and a thermal neutron beam of 9.0 × 109 nth/cm2·s intensity with low fast-neutron dose (1.0 × 10−13 Gy·cm2/nth) and gamma dose (<1.0 × 10−13 Gy·cm2/nth). Both neutron beams will be forward directed. Each beam can be turned on and off independently through its individual shutter. A complete NCT treatment using the designed epithermal or thermal neutron beam would take 30 or 20 min, respectively, under the condition of assuming 10 µg 10B/g in the blood. Such exposure times should be sufficiently short to maintain near-optimal target (e.g., 10B, 157Gd, and 235U) distribution in tumor versus normal tissues throughout the irradiation. With a low operating power of 300 kW, the heat generated in the core can be removed by natural convection through a pool of light water. The proposed design in this study could be constructed for a dedicated clinical NCT facility that would operate very safely.