Calcium-ion batteries (CIBs) are considered to be promising next-generation energy storage systems because of the natural abundance of calcium and the multivalent calcium ions with low redox potential close to that of lithium. However, the practical realization of high-energy and high-power CIBs is elusive owing to the lack of suitable electrodes and the sluggish diffusion of calcium ions in most intercalation hosts. Herein, it is demonstrated that calcium-ion intercalation can be remarkably fast and reversible in natural graphite, constituting the first step toward the realization of high-power calcium electrodes. It is shown that a graphite electrode exhibits an exceptionally high rate capability up to 2 A g−1, delivering ≈75% of the specific capacity at 50 mA g−1 with full calcium intercalation in graphite corresponding to ≈97 mAh g−1. Moreover, the capacity stably maintains over 200 cycles without notable cycle degradation. It is found that the calcium ions are intercalated into graphite galleries with a staging process. The intercalation mechanisms of the “calciated” graphite are elucidated using a suite of techniques including synchrotron in situ X-ray diffraction, nuclear magnetic resonance, and first-principles calculations. The versatile intercalation chemistry of graphite observed here is expected to spur the development of high-power CIBs.