This paper introduces a new single-phase ac-ac converter according to an impedance network. The introduced topology retains the excellences of the conventional non-isolated single-phase ac-ac Z-source converter (ZSC), including buck- boost ability and capability of reversing and maintaining of the phase angle. The suggested converter hires coupled inductors to control output voltage by adjusting its turns ratio along with duty ratio. By utilizing unique shape of coupled inductors, the introduced converter can acquire high voltage boost capability by reducing turns ratio which leads to cost and size reduction. Unlike the single-phase ac gamma source converter, the input current in the introduced converter is continuous. As a result, it does not suffer from non-sinusoidal high THD input current. The voltage and current spikes across the switches are removed by a safe commutation strategy. The introduced converter can be exploited as a dynamic voltage restorer for voltage sag and voltage swell compensating. Simulation results in MATLAB are supplied to survey the converter's operation.