Using Monte Carlo methods the response matrix of a Bonner sphere spectrometer with a 6LiI scintillator has been calculated. The response functions were calculated for the bare detector and for polyethylene spheres 5.08, 7.62, 12.7, 20.32, 25.4, and 30.48 cm in diameter. Twenty-three beams of monoenergetic neutrons were used as sources in the energy interval from 0.025 eV to 100 MeV. The response functions were interpolated to energy points of those calculated in earlier literature works and compared with two response functions reported in the literature; good agreement was found from this comparison. The main differences were found for neutrons with energies higher than 20 MeV and, to a minor extent, for low-energy neutrons as well. These differences are mainly attributed to the cross-section libraries utilized in the different studies.