Physical field mapping problem is generally faced in multi-physics coupling calculations, and multi-region (usually divided by different physical properties) coupling further increases the problem’s difficulty. The multi-region algorithm can achieve the solid–fluid conjugate heat transfer for the multi-region Neutronic and Thermal-Hydraulic (N-TH) coupling calculation. This paper proposed a multi-region algorithm for solving neutronic fields and further coupled it with multi-region heat transfer in OpenFOAM. The multi-region algorithm solves the neutron transport equation region-by-region and establishes a new coupling boundary condition to eliminate the obstacles to communication between adjacent regions. The multi-region algorithm is developed in OpenFOAM as a neutron transport solver and verified by the 2D-IAEA, 2D-TWIGL, and the 3D-TAKEDA benchmarks. The multi-region neutron transport solver and the original Conjugate Heat Transfer (CHT) solver are coupled to establish a multi-physics coupling platform. Hence, the multi-physics solver can provide pin-by-pin neutronics and thermal hydraulics results for multiple regions (including solid or fluid regions) based on the same set of grids. The geometric adaptability and parallel performance of the coupling platform are superior, which depends on the inherent characteristics of the OpenFOAM platform. The coupling platform is used to perform N-TH coupling calculations for the Nuclear Thermal Propulsion (NTP) reactor's Low Enriched Uranium (LEU) assemblies, demonstrating the coupling calculation capability of the multi-region algorithm for complex reactor geometry systems. The calculation results show intense N-TH coupling effects in the NTP assemblies, which can provide an essential reference for nuclear thermal propulsion reactor design.