First-principles calculations were carried out for the alkali (Li, Na, K) metal-graphite intercalation compounds (AM-GICs). From the calculated formation energies (ΔE) of the AM-GICs, it was determined that each Li-GIC and K-GIC were energetically stable until the high alkali metal density LiC6 and KC8. On the other hand, even the low Na density NaC16 and NaC12 are already not stable. Furthermore, the NaC8 and NaC6 are unstable. It has been experimentally reported that Na hardly intercalates into the graphite contrary to the Li and K. Our calculation results agree with these facts. In addition, based on the calculated energy barriers of the Li, Na and K ion jumps between sites in the graphite, it can be deduced that larger radius ions more smoothly diffuse in the graphite.