Of all the isolated power converters, flyback converter is widely used for low power electrical appliances, since its property of the simple circuit topology, low cost, and fewer components. Zero-voltage-switching quasi-resonant flyback converter (ZVSQRC flyback), which is able to realized soft switching technique, has several advantages compared with conventional flyback converter, but it still possesses the merits of flyback converter. In this thesis, the operation of ZVSQRC flyback operated in critical conduction mode is investigated in detail. Besides, the designing procedure including power stage circuit and control loop is proposed. Finally, a ZVSQRC flyback with rated power of 80W is implemented to verify the theoretical analysis.