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In this paper, a fuzzy logic controller has been developed to obtain a stable current output adjusting the modulation index of a multilevel converter in a variable speed wind turbine system. The variable speed wind turbine system has been modeled containing a squirrel-cage induction generator (SCIG), and SPWM controlled AC-DC-AC converter which is constituted of a 6-pulse rectifier and 3-level multilevel inverter. The simulation of the power conversion system has been evaluated using Matlab/Simulink and Fuzzy Toolbox. The input parameters have been modeled with a variable voltage-variable frequency (VVVF) generating system according to various wind speeds. The input values of converter have been limited between 350-700 V and 40-60 Hz. The fuzzy logic controller tracks the input values and controls the converter in order to supply desired current output. The control process has been developed selecting the most accurate modulation index for multilevel inverter which directly affects the output power.