Recently, multilevel inverters have attracted the attention of different electric transportation industries due to the possibility of increasing the dc-link voltage. Flying Capacitor (FC) multilevel inverter is an efficient structure that does not need different dc sources and is therefore suitable for electric vehicle applications. Moreover, Model Predictive Control (MPC) is a well-known control strategy for different electric drive systems like induction machines. However, MPC of electrical machines supplied with a multilevel FC inverter has not been investigated yet.As a result, this paper concentrates on the predictive control of an IM drive with 4-level FC inverters. The application of this control strategy is simple and many objective functions can be simultaneously taken into account in the optimization of the cost function, such as the dynamic tracking behavior and the voltage balancing of the FCs. To compensate the delay time which emerges due to a large number of calculations in each sampling instant, delay compensation method has been utilized. According to the results, the proposed predictive control of the IM drive with a 4-level FC inverter offers fast dynamic behavior with no overshoot, low torque and current ripples, and perfect voltage balancing of the FCs.