A　circuit　configuration　and　circuit　topological　family　of　the　current　(Boost)　mode　AC-AC　converter　with　high　frequency　link　are　proposed.　This　kind　of　circuit　topology　is　constituted　of　storage　inductor,　input　cycloconverter,　high　frequency　transformer,　output　cycloconverter,　as　well　as　input　and　output　filter.　The　steady　principles　and　phase-shifting　control　strategy　are　deeply　investigated,　the　magnetic　saturation　of　storage　inductor　in　this　kind　of　converter　at　start-up　and　the　voltage　spike　of　the　high　frequency　transformer＇　leak　inductance　are　proposed　and　solved.　The　simulation　and　principle　verification　of　the　kind　of　converter　are　given.　The　research　results　have　demonstrated　that　this　kind　of　converter　has　the　advantages　such　as　high　frequency　electrical　isolation,　simple　topology,　two-stage　power　conversions　(LFAC-HFAC-LFAC),　bi-directional　power　flow,　high　conversion　efficiency,　high　line　power　factor,　strong　load　adapting　ability　and　high　reliability　during　short　circuit　in　load.