Boron Neutron Capture Therapy (BNCT) is a promising form of radiotherapy expected to be effective in treating refractory cancers such as glioblastoma. A key factor in BNCT is the neutron energy spectrum in the epithermal range (0.5 eV-10 keV), which is challenging to evaluate due to its broad and low-energy characteristics. This study proposes a novel measurement method for the neutron energy spectrum in the epithermal range, utilizing a combination of activation foils and a position-sensitive proportional counter to capture the full energy range of neutrons in BNCT. A prototype of the spectrometer was developed, and numerical validation was performed. The results of the numerical study demonstrated that the proposed spectrometer can accurately evaluate the neutron energy spectrum across a broader energy range compared to existing methods.