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Idea of Quasi-Z-Source converter gets for Z-Source converter. The Quasi-Z-Source Inverter was suggested in 2007. This power converter has total ability of Z-Source converter and can be used to implement dc-to-ac, ac-to-dc, ac-to-ac, and dc-to-dc power conversion. Quasi-Z-Source converter employs a unique impedance network (or circuit) to couple the converter main circuit to the power source. Other benefits Quasi-Z-Source are: Continuous input current ,Decrease capacity of element such as inductor and capacity in Z-network ,High voltage gain .
 The Quasi-Z-Source converter overcomes the conceptual and theoretical barriers and limitations of the traditional voltage-source converters. One of its features is the ability to increase the input voltage to a preferred level. To describe the operating principle and control, this paper focuses on an example: a Quasi-Z-Source converter for dc-ac power conversion. The first section describes Quasi-Z-Source converter parts and its operation principles. Next section first describes the fundamental concepts of Fuzzy Logic. Fuzzy Logic is a new way of thinking and describing things and for implementation of intelligence and smart machines and industrial robots whose basics are like the human kind. In the next chapter simulate the Quasi-Z-Source converter with Fuzzy control method.