Single-phase compound AC-AC converters are increasingly being recognized for their capability to perform voltage and frequency conversion without the necessity of DC-bus energy storage components. However, existing research still faces challenges such as excessive high-frequency switches and current discontinuity. A Cuk-type single-phase AC-AC converter is proposed in this article. It allows for both bucking and boosting of the input voltage with the ability to operate at a step-changed frequency, offering a broad range of voltage and frequency regulation. Besides, it is featured with low power loss and high efficiency for there are only six switches used and only one switch works at high frequency. Additionally, it acquires natural commutation capability without additional snubber circuits or complex commutation control strategies. Furthermore, the input and output currents are continuous, obviating the need for additional input or output filters and thus enhancing power density. The operation principle and circuit analysis are detailed within. To validate the converter's feasibility, a 200W laboratory prototype has been built and experiments have been conducted in both buck and boost modes at output frequencies of 25Hz, 50Hz, and 100Hz, demonstrating the converter's effectiveness.