The computerized simulation of the reactor core is one of the significant steps necessary for designing a nuclear power plant. So far, very suitable Monte Carlo–based codes have been developed (e.g., MCNP, TRIPOLI, KENO, OpenMC, etc.) for the neutronic simulation of the reactor core. In this study, an approach based on Geant4, as an extendable code with the capability to provide a comprehensive reactor core design tool, is developed to calculate the effective multiplication factor (keff) and neutron flux distribution. A combination of the Geant4 code and the NJOY code is applied to calculate the temperature-dependent cross-section library. The C5G7-1D, the Godiva critical facility, and the Jordan subcritical reactor are examined as a benchmarks/case study. The results of the calculation of keff (i.e., relative error < 0.1%) and flux distribution (i.e., relative error <3%) are in very good agreement with the calculation results of the MCNP code and the experimental results. The extensions for the calculation of thermodynamic/thermohydraulic effects as well as the calculation of electron/photon transport and reactor dynamics are under development and will be reported as subsequent results.