A charging system capable of charging a battery cell so that the surface temperature of the battery cell does not exceed an upper temperature limit, is provided. A battery charger is configured in a manner such that a setting current is variable during charging. The battery charger starts charging of a secondary battery with a setting voltage set to a minimum charging current value. The surface temperature of the secondary battery is measured during charging. An estimated temperature value is calculated which is a surface temperature of the secondary battery, at which the secondary battery is charged up until a charging amount corresponding to the maximum surface temperature under assumption that the charging is performed with a present charging current value. The setting current is increased when the estimated temperature value is lower than the target temperature range and is reduced when the estimated temperature value is higher than the target temperature range. When the estimated temperature value belongs to the target temperature range, a present setting current is maintained.