A new approach has been suggested to establish reliable response matrix of a CRNA Bonner Sphere Spectrometer equipped with a high efficiency 10 mm diameter × 2 mm thick 6LiI (Eu) scintillation detector from thermal neutron energy up to 20 MeV. It combines the experimental response functions obtained using a continuous neutron spectrum emitted from an 241Am-Be neutron source of known emission, with those obtained by Monte-Carlo (MC) calculations. Sensitivity analysis has been performed to check the influence of pertinent parameters on the MC computed detector response. The parameters of interest are the density of polyethylene moderators, the cross section library used in MCNP5 and two computing models depending on the interactions of the neutrons in the detector. The calculated responses of the spectrometer to the 241Am-Be neutron source showed discrepancies depending on the sphere diameter when compared to our measured responses. However, this difference was smaller compared with the experiments available in the literature. The enhancement achieved in the present study is partly due to improved modeling in the MC calculations. To correct for the differences observed, a fitting factor has been deduced for each sphere diameter and used to adjust the MC responses to the experimental ones. The obtained results were subsequently compared to the experimental data of GSF-G spheres system obtained for a typical 4 mm diameter × 4 mm thick 6LiI scintillator for four ISO-8529 selected neutron energies (144.0 keV, 565 keV, 2.5 and 14.8 MeV). The present responses were similar in shape but higher, in absolute values, by about two and half times for all spheres owing essentially to the increase in active part of the detector. Finally, the CRNA-BSS response matrix containing 48 energy points from 0.01 eV to 20 MeV for 22 sphere diameters with a mean polyethylene density of 0.944 g/cm3 was constructed by applying a spline interpolation method. The released response matrix was then compared to data available in the literature evaluated by Monte-Carlo calculations for a 4 mm × 4 mm 6LiI crystal scintillator. The obtained response matrix is intended for radiation protection applications at CRNA.