This paper presents a fuzzy logic controller to vary the voltage transfer ratio of Quasi Z Source Indirect Matrix Converter (QZSIMC) for application in induction motor drive during unbalanced input voltage and variable drive speed. A fuzzy logic controller achieves the variation of the voltage transfer ratio from 0.866 to 5 by modifying the shoot through duty ratio of the quasi z source network. Modification in the shoot through duty ratio of the rectifier results in the improvement of the voltage boost factor of the quasi network which in turn varies the voltage transfer ratio. The fuzzy controller varies the shoot through duty ratio with input voltage error and set speed error. The proposed fuzzy-based QZSIMC can attain variable boost as well as buck function with variable shoot through duty ratio. Thus, this proposed method overcomes the limitation of constant boost. The proposed fuzzy-based QZSIMC widens the operating range of the induction motor during all the input voltage sag conditions and reduces the stress on the switches. The simulation results validate the quality performance of the proposed induction motor drive.