Thermal conductivity of frozen soil is a crucial property that influences heat transfer rate and freezing depth during the freezing process. However, accurately evaluating frozen soil's thermal conductivity is challenging due to its complex compositions and structures. To address this challenge, this study proposed the frozen soil quartet structure generation set (FSQSGS) to generate reasonable representative volume elements (RVEs) of frozen soil. The FSQSGS incorporates the ice phase and accounts for the freezing process, with clear physical meanings of input parameters. Then, the soil thermal conductivity of RVEs is calculated by the lattice Boltzmann method (LBM). This proposed calculation method is validated by experimental and analytical results of soil samples with various textures. The verification shows the broad applicability of the proposed model, especially for soils with fine grains or high saturation. Further, the influence of soil components and pore-scale geometry on the soil thermal conductivity is analyzed, with direct visualization of heat transfer. Results show that despite the soil skeleton geometry, i.e., the granular size and anisotropy, soil components have important effects on the soil thermal conductivity. Contents and thermal conductivity of soil particles are the main factors, while water and ice filling soil pores provide pathways for heat conduction, thereby improving thermal conductivity.