Cointercalation systems consisting of graphite, sodium, and some linear glycol ethers (glymes) are anticipated for use as negative electrodes in sodium ion batteries because of their superior properties such as outstanding cycle performance. We synthesized a ternary intercalation compound consisting of sodium, deuterated diglyme (diglyme-d(14)), and graphite by a solution reaction. Then we investigated the dynamics and coordination structure of diglyme-d(14) molecules by H-2 solid-state NMR. Two diglyme molecules coordinate to each sodium ion rigidly, except for rotation of the methyl groups at low temperatures below 233 K. At room temperature, diglyme weakly coordinates to a Na ion through one oxygen atom of the ligand and rotates around the ONa axis. The active motion of sodiumdiglyme complexes is favorable for Na diffusion between graphene layers in the graphite intercalation compound.