In this paper, a predictive torque control (PTC) algorithm is introduced for controlling an induction motor (IM) fed by a bidirectional quasi Z-source inverter (BQZSI). A torque, stator flux and capacitor voltage magnitudes control algorithm evaluates a cost function, based on a simple discrete models of the IM and the BQZSI, for each BQZSI available switching state. The voltage vector with the lowest torque, a stator flux and capacitor voltage magnitude errors is selected to be applied in the next sampling interval. The proposed PTC algorithm, with its single structure, can control both sides of the BQZSI to optimize the motor performance with an extremely simple and versatile control algorithm and without any dynamic response limitation caused by the cascaded control structure. A high degree of flexibility is obtained with the proposed control technique due its online optimization algorithm. This paper proposed a new adjustable speed drive system based on a three-phase BQZSI feeding an induction motor. Where, the interesting advantages of the PTC algorithm are combined by the advantages of one of the most interesting power electronics converters, the BQZSI. Simulation results for a 4 kW IM are presented to validate the new proposed electrical drive system.