Li/Na organic batteries have attracted the attention of researchers because of their flexibility, lightweight, and recyclability compared to the metal oxide‐based Li/Na‐ion batteries. The low specific capacity is a major problem for the application of Li/Na organic batteries. Herein, we found that the green and natural gallic acid derivatives, ellagic acid (EA, dimer) and tannic acid (TA, oligomer) are good anode materials for Li‐ and Na‐ion batteries due to their π‐π conjugated structures and abundant carbonyl, carboxyl, phenolic groups. Outstanding electrochemical performance in specific capacity and cycling stability are exhibited. 644, 364, 195, and 162 mAh g−1 for EA and 297, 451, 465, and 265 mAh g−1 for TA are obtained for Li‐ion batteries (LIBs) at current densities of 0.1, 0.2, 0.5, and 1.0 A g−1 after 150, 250, 500, 1000 cycles, respectively. The specific capacities of EA and TA LIBs are higher than those of organic LIBs and can be comparable with metal oxide LIBs. And the cycling stabilities of EA and TA LIBs are better. Meanwhile, EA and TA are universal anode materials, which enable us to construct Na‐ion batteries that show specific capacity of 105 mAh g−1 for EA and 46 mAh g−1 for TA at 50 mA g−1 after 350 cycles. This work provides us important inspirations for exploring organic materials from nature, which can be applied in green and high‐performance energy‐storage devices.