The feasibility of using the HEC-1 beam port of the IRT-T research reactor to generate an epithermal neutron beam for Boron Neutron Capture Therapy (BNCT) was investigated using MCNPX2.6 Monte Carlo simulation. The reactor was first simulated to design and optimize a Beam Shaping Assembly (BSA) that meets the neutron beam criteria recommended by the International Atomic Energy Agency (IAEA). The suggested BSA configuration consisted of a cylindrical geometry with 25 cm of MgF2 and 15 cm of Fluental® as a moderator, 15 cm of Pb as a reflector, two 5 cm Bi slabs as gamma-ray shields, and 4 mm of 6Li and 5 mm of borated polyethylene sheets as thermal neutron filters. The results showed that the epithermal neutron flux at the BSA exit was 2.3×109 n/cm2.s, and in-phantom dose analysis indicated that the designed beam could be used for the treatment of deep brain tumors within an allowable treatment time of 50 min.