Using the Geant4 software package, a numerical simulation of a neutron source of the time-offlight spectrometer GNEIS created on the basis of the SC-1000 synchrocyclotron with 1 GeV proton energy at the NRC Kurchatov Institute—PNPI (Gatchina) has been carried out. The influence of the structural features of the neutron source of the spectrometer on the spatial and energy distributions of neutrons has been studied. The intensity and spectral characteristics of the neutron flux in the range of 1–1000 MeV have been determined on the basis of the obtained information and detailed allowance for all elements of the neutron beam guide system. It is found that the best agreement between the experiment and calculation performed by means of Geant4 is observed when using the QGSP_INCLXX_HP model. In the neutron energy range of 1–200 MeV, the difference between the experimental and calculated shapes of the spectra is less than 25%.