Provided are a control circuit and a delay circuit. The control circuit includes a control unit, a first feedback unit, and a second feedback unit. The first feedback unit outputs a first feedback signal according to a voltage of the control unit and a first reference voltage. The second feedback unit outputs a second feedback signal according to a voltage output by the first feedback unit and a second reference voltage. The control unit is configured to adjust a voltage of the second terminal of the control unit according to the first feedback signal and adjust a voltage of a third terminal of the control unit according to the second feedback signal, to make a change value, changing along with a first parameter, of a current of the control unit be within a first range.