In this study, it has been focused on a fractional version of a chaotic system that is defined by three state variables, is autonomous and has a multi-wing atractor characteristic. The minimum fractional-order of this multi-wing and fractional-order chaotic system has been determined by the stability analysis. The numerical response of this system has been obtained by the Grünwald-Letnikov method by selecting a fractional order that is higher than the determined minimum fractional degree. Then, a third-order approximation function is calculated for this chaotic system by using the Matsudo method, and an imitation circuit has been designed by using this calculated function. This designed circuit has been adapted to the circuit structure that is proposed for the multi-wing chaotic system. The efficiency of the obtained final circuit has been verified by comparing the numerical simulation results and the responses of the revealed circuit structure.