Abstract: Due to the complexity of neutron transport simulation and the difficulty of its coupling calculation with other physical processes, the full-core detailed neutron transport-thermal-hydraulics multi-physical calculation is a difficulty of reactor engineering. Based on the finite volume C++ open source software OpenFOAM, this work establishes the numerical solution models of steady-state and transient neutron transport kinetic equations by using the finite volume method, and develops the neutron transport kinetics solver ntkFoam. The simulations of some benchmark problems show that the proposed ntkFoam solver can simulate the neutron transport kinetics problems accurately, and can adapt well to different dimensions and complicated geometries. The detailed coupling calculation of neutron transport and heat-mass transfer processes can be realized, which can provide some detailed coupling thoughts and techniques for neutron transport based full core multi-physical simulation.