Nowadays, the global trend is towards reducing CO2 emissions and one solution is to replace internal combustion vehicles with electric vehicles. To this end, electric drive system, the most crucial part of an electric vehicle, has gained importance and has become a major research field. The induction motor (IM) is one of the best candidates for electric vehicle applications due to its advantages such as having simple and robust design, its low cost maintenance requirements and the ability to operate in harsh environments. However, it has a highly nonlinear model with time- varying electrical and mechanical parameters making them difficult to control. Finite control set-predictive torque control (FCS-PTC) is an inherently suitable and a promising control method for the IM because FCS-PTC is easy to implement and has the ability to handle nonlinearities with the inclusion of constraints. In addition, the elimination of speed sensors increases the reliability of electric motor drives while reducing cost and hardware complexity. In this paper, a speed-sensorless FCS-PTC based IM drive system is designed in order to combine the aforementioned advantages. Unlike the current literature, to improve the torque response of conventional FCS-PTC, the load torque is also estimated by an adaptive fading extended Kalman filter and is fed back into the torque control loop. The results show that improved control performance is achieved.