A control circuit and an AC-DC power supply are provided. A ripple reference signal characterizing an industrial frequency ripple component of an output voltage is added to a reference voltage of a desired output voltage, so that a reference and a feedback voltage of the output voltage are almost the same at the industrial frequency band. In addition, a voltage compensation signal outputted by an error compensation circuit does not include the industrial frequency ripple component, and the voltage compensation signal without the industrial frequency ripple component does not affect a tracking reference of the current loop. Therefore, the loop can be designed without considering limit of the industrial frequency on a cut-off frequency of the loop, thereby effectively increasing the cut-off frequency of the loop and improving a dynamic response speed of the loop.