A new type of single-phase Z-source AC/AC converter based on a single-phase matrix converter is proposed in this paper. The proposed single-phase Z-source AC/AC converter has unique features; namely that the output voltage can be bucked and in-phase/out-of-phase with the input voltage; that the output voltage can be boosted and in-phase/out-of-phase with the input voltage. The converter employs a safe-commutation strategy to conduct along a continuous current path, which results in the elimination of voltage spikes on switches without the need for a snubber circuit. The operating principles of the proposed single-phase Z-source AC/AC converter are described, and a circuit analysis is provided. To verify the performance of the proposed converter, a laboratory prototype based on a TMS320F2812 DSP was constructed. The simulation and the experimental results verified that the output voltage can be bucked-boosted and in-phase with the input voltage, and that the output voltage can be bucked-boosted and out-of-phase with the input voltage.