A novel circuit topologies family of the current mode AC/AC converter with high frequency ac link, based on Flyback converter, are proposed. These circuit topologies which can transfer one unregulated sinusoidal voltage with high THD into another regulated constant frequency sinusoidal voltage with low THD, are constituted of input cycloconverter, high frequency storage transformer and output cycloconverter. The circuit topologies family include single four-quadrant power switch mode, push-pull mode, half-bridge mode,and fullbridge mode circuit. The single four-quadrant power switch mode and push-pull mode converter are suit for low input voltage fields, but the half-bridge mode and fullbridge mode converter are suit for high input voltage fields. The operational mode, steady principle and transient voltage feedback control strategy of the kind of converter are investigated. The output characteristic curve, its relation to internal resistance, and the design criterions for the key circuit parameters are given. The current mode AC/AC converters with high frequency ac link have the advantages such as simple topology, two-stage power conversions, bi-directional power flow, high frequency electrical isolation, good line current waveform, strong load adapting ability. The correction and advance of the converters are verified by the Pspice simulation and test results.