In order to explore the pore structure damage characteristics of the sandstone in the cold region under the freeze-thaw cycle, the nuclear magnetic resonance(NMR) test was carried out on the red sandstone samples undergoing different freeze-thaw cycles. Combining the multifractal theory, the evolution law of the pore structure in red sandstone at different scales under freeze-thaw cycles was explored. The results show that the freezing and thawing promotes the development of pore structure of red sandstone. The T₂ spectrum of red sandstone without freeze and thaw shows 3 peaks, and 4 peaks appeared in the T₂ spectrum of freeze-thaw red sandstone. It reflects the complex pore structure evolution of red sandstone during freezing and thawing. Mono-fractal does not characterize the pore structure of red sandstone micro-pores. However, both the micro-pores and medium macro-pores of red sandstone have good multifractal characteristics. Multifractal parameters are highly linearly associated with porosity. In the micro-pores, mono-fractal dimension D₂ is negatively correlated with the porosity, the overall heterogeneity parameters D(0) - D(1) and low probability parameters D(- 10) - D(0) negatively correlated with porosity, the Hurst index H is positively correlated with porosity. In the macro-pores, D(0) - D(1), D(- 10) - D(0) and H are positively correlated with porosity. The evolution of freeze-thaw red sandstone is analyzed by multi-fractal, it provides a basis for further study of the damage mechanism of freezing-thawing red sandstone.