A control circuit of a multi-phase converter can include: an inductor current sampling circuit configured to generate a plurality of sampling signals corresponding to a plurality of channels of the multi-phase converter, where each of the sampling signals characterizes an inductor current of a corresponding channel; an error circuit configured to generate a plurality of error signals corresponding to the plurality of channels, where each of the error signals characterizes an error between the inductor current of the corresponding channel and a reference current; and a modified circuit configured to modify the sampling signals of the corresponding channels according to the plurality of error signals to generate a plurality of modified sampling signals, where the control circuit balances the inductor currents between the plurality of channels according to the plurality of modified sampling signals.