This invention aims at providing a control circuit of power supply in which a secondary battery and a device are connected in parallel, to output capable of preventing over-charging of the secondary battery and supplying power from the secondary battery to the device, and a control method of the power supply. A device 5G and a secondary battery 2G are connected to a DC-DC converter 1G in parallel. The device 5G is supplied with both a power from the DC-DC converter 1G and a power from the secondary battery 2G. When the secondary battery 2G is in non-charging state, an offset circuit 15G supplies a positive offset for reducing a difference of voltage between a detection signal Vx1G and reference voltage e1G to a reference voltage e1G corresponding to a charging inhibit signal CAS. An error amplifier ERA1G reduces an actually flowing charging current CCG by an amount corresponding to the offset value as a result of recognizing that the charging current CCG flows more by the amount corresponding to the offset value.