The Back-n facility at the China Spallation Neutron Source (CSNS Back-n facility) is a newly-built time-of-flight (TOF) spectrometer for neutron nuclear data measurements. The Energy Resolution Function (ERF) of a neutron spectrometer is essential for the analysis of the data measured on the facility, especially in the resolved energy region, as the ERF represents the intrinsic broadening effect of the measured resonance peaks. For the constructing of the ERF, the most crucial component need to be investigated is the neutron production and transport in the spallation target, which could only be inferred from detailed Monte-Carlo simulations. In the present work, the simulation is performed with the Monte-Carlo toolkit Geant4 on account of its flexible features of particle tracking and parameter recording. The production and transport of neutrons in the target–moderator–reflector (TMR) assembly of the Back-n facility are simulated, and the simulation data are analyzed to deduce the distributions of the time spent of neutrons’ transport in the TMR assembly. Based on the distributions of neutrons with different energies from eV to MeV, the ERF of the Back-n facility is constructed by adapting the RPI resolution function-form which is extensively used in neutron nuclear data evaluation. The energy dependence of the ERF is also parameterized to ensure its applicability for the nuclear data evaluation in the resolved energy region. Furthermore, the standard neutron capture cross section of ¹⁹⁷Au is taken to verify the accuracy of the ERF by comparing the measured data and the theoretical ones from the ENDF/B-VIII.0 library.