A method and an apparatus for charging a lithium-ion based rechargeable battery in a short time is provided. A terminal voltage of the rechargeable battery is compared with a predetermined first set voltage V1 while charging the rechargeable battery with a constant current; pulse charging is performed in which charging is halted after the rechargeable battery is charged with the constant current only during a predetermined first set time T1 when the terminal voltage becomes the first set voltage V1 or more; both an elapsed time An from the start of the halt and a terminal voltage Bn at the elapsed time An are measured a plurality of times during the halt of charging in the pulse charging and the terminal voltage Bn is compared with a predetermined second set voltage V2; whether or not the terminal voltage drops to the second set voltage V2 or less is presumed based on measurement results of the elapsed time An and the terminal voltage Bn in the case where the terminal voltage Bn is higher than the second set voltage V2 when the elapsed time An reaches a predetermined second set time T2; both the pulse charging and the presumption of the terminal voltage are repeated when presumed that the terminal voltage drops to the second set voltage V2 or less; and charging is ended when presumed that the terminal voltage does not drop to the second set voltage V2 or less.