Activated carbon cold adsorbed H2 storage (CAH2) is a promising physical hydrogen storage method. However, conventional storage tanks face problems of local high heat accumulation during the cold adsorption process, leading to low hydrogen storage efficiency and capacity. This study attempts to design high thermal conductivity fins to a conventional CAH2 tank to enhance heat and mass transfer, thereby promoting the hydrogen adsorption process. An accurate mathematical model and finite element method are established to calculate the CAH2 process. The influence mechanism of different fin arrangements, fin length, fin number (spacing), and fin width on the temperature field, adsorption concentration field and storage performance are explored. The results show that adding fins can effectively promote heat transfer and suppress local high temperature and low adsorption concentration areas. When the adsorption mass reaches 0.05 kg, the storage efficiency of the three tank schemes with added fins improves by approximately 40% compared with the original tank. Although extending the fin length will enhance heat conduction, it will also suppress the heat convective transfer effect. The optimal fin length is found to be 30 mm. Increasing the number of fins (reducing spacing) can significantly decrease the areas of local high temperature and low adsorption concentration, but this beneficial effect diminished when the number of fins exceeded 14. Increasing the fin width has a weaker beneficial effect on the temperature field and adsorption concentration field, and also cause a significant reduction in the tank volume, thereby reducing the total hydrogen storage capacity. The findings of this study can provide important guidance for the application of high thermal conductivity fins in CAH2 tanks.