Abstract: Thermal-hydraulic calculations for pebble-bed high-temperature gas-cooled reactor (PB-HTGR) differ significantly from those of pressurized water reactor (PWR), due to factors such as large computational scales, significant temperature variations, and cylindrical geometry. PB-HTGR features a porous-medium core structure, and the fuel temperature calculations require a multi-scale approach, covering the entire core, fuel pebbles, and TRISO particles. This study aims to address the limitations of existing thermal-hydraulic analysis programs, improve computational efficiency for PB-HTGR simulations. Compared to the fine mesh finite volume method, the nodal methods allow the use of larger mesh sizes and has higher computational efficiency. The nodal expansion method (NEM), as a type of nodal method, is typically used for solving neutron diffusion equations. Based on the formal consistency between the neutron diffusion equation and the thermal conductivity equation, this study applied NEM to calculate the full-core thermal conduction of the PB-HTGR. The Legendre polynomial was used to perform second-order expansion on the temperature in all directions, and the nodal temperature was iteratively solved. Based on the above method, a corresponding computational program, TH-NEM, was developed to solve the solid temperature field in PB-HTGR. Additionally, a bi-quadratic polynomial reconstruction method was employed to calculate the node temperature, which was mapped from the average temperature of each mesh, facilitating the coupling of TH-NEM programs with other programs. Numerical simulations were performed for pure solid model, porous media model, and the HTR-PM model. The numerical simulations using TH-NEM show good agreement with reference values for all models tested. Compared with the fine mesh method, TH-NEM achieves higher computational efficiency under the condition of ensuring the computational accuracy. The preliminary results demonstrate that TH-NEM can be used for solid heat conduction calculations in PB-HTGR. The method provides an efficient approach for thermal analysis while maintaining accuracy, making it suitable for large-scale core simulations.