The improvement of power quality at the supply side and the motor side for induction motor drives (IMDs) is always an industrial key interest. The traditional pulse width modulation (PWM) technique used in switching and controlling the IMDs greatly influences the grid power quality. In this paper, a new modified level shifted carrier based PWM technique is proposed for a multilevel inverter (MLI) based IMDs. A 36-pulse diode bridge rectifier is used at the input side of the inverter to suppress the total harmonic distortion (THD) of the supply current. The proposed PWM technique utilizes third harmonic injection technique with inverted sinusoidal carrier signals to form the four level shifted carrier signals for the 5-level (5L) modular multilevel cascaded (MMC) inverter, which is named as third-harmonic injected inverted sinusoidal carrier PWM (THI2SCPWM). The THI2SCPWM offers low supply current THD, low inverter line voltage THD, low stator current THD, high input power factor and smooth dynamic response of the IMD compared to the existing PWM techniques. The performance of the proposed THI2SCPWM technique is verified in MATLAB/Simulink in terms of starting behavior, speed control, load perturbation, and variation of the load and speed of the IMD.