Normally, the design of the cryogenic structured packings mainly relies on the hydraulic experiments of room temperature fluids such as water due to the difficulties and high cost of conducting cryogenic experiments. This may result in significant performance discrepancies in cryogenic distillation applications since cryogenic fluids have quite different properties. In this work, with the help of the CFD combing VOF method, a three-dimensional structured packing model of counter-current flow was established. The flow characteristics and mass transfer performance of the LN2-O2 system (liquid nitrogen and gaseous oxygen) under different packing parameters including B (base), S (side), H (height), and β (crimping angle) were comprehensively coupled and analyzed. In particular, the flow morphology, and local wetting rate were analyzed to reveal the differences in flow characteristics between the LN2-O2 system and the water–air system. Furthermore, the mass transfer coefficient, mass transfer rate, and pressure drop of the LN2-O2 system were analyzed to obtain a deep understanding of the cryogenic distillation process under different packing geometric parameters. According to the results, the flow of the water–air system and LN2-O2 system is significantly different. As the specific values of base B, side S, and height H decrease, the water remains in rivulet flow, while LN2 changes from film flow to rivulet flow, which indicates the effect of the contact points on the flow of liquid nitrogen is more significant than that of water. With a constant specific surface area, as the crimping angle β increases from 60°to 120°, the wettability of liquid nitrogen on the suspended surface can be significantly improved. The wetting rate of LN2 increases by 9.78%, resulting in the mass transfer rate increasing by 9.02%, and the wet pressure drop decreasing by 9.60%. It shows the structured packing with the higher crimping angle β of 120° has a good application prospect in cryogenic distillation.