The band electronic structures of polyphenanthrene (PPh) and polyacene (PA) doped with lithium are calculated and analyzed at the extended Huckel level of theory to elucidate the lithium storage mechanism in amorphous carbon (a-C) electrode materials used for the lithium-ion rechargeable battery. The undoped, LiC8, LiC4, and LiC2 stages for both polymers are computed and analyzed. PA-type moieties in a-C materials should be doped preferentially in the initial stages of doping because of the deep unoccupied levels relevant to the PA-type edge structure. PPh should possess greater doping capability than PA especially in heavy doping stages, because there is a high density of states (DOS) above the Fermi level in PPh. The Fermi levels of PPh(LiC2) and PA(LiC2) lie just below the Li bands; thus, the upper limit of Li doping in a-C materials is likely the LiC2 stage. The irreversible capacity loss observed in the charging-discharging process in a-C materials may be attributed to the low-lying levels relevant to the PA-type edge structure.