This paper deals with the development of a V/F control of an induction motor with THD optimization using cascaded multilevel converters. The optimization algorithm was a genetic algorithm, which allows to obtain a voltage vs. frequency ratio (V/F) that decreases the voltage value as the frequency is reduced by maintaining the total harmonic distortion (THD) at levels very close to 0% over the entire frequency range of operation. The power converter is a common-source cascaded H-bridge multilevel inverter with maximum 15 steps per line voltage. The inverter was simulated by supplying a three-phase induction motor. The result of the simulations allows verify the optimization of the THD throughout all of the frequency operation range.