Three phase induction motors have been widely used in many industrial applications. e.g., on the electrical vehicle for creating traction process. The motor should be able to track the reference to maintain the good output. Therefore, the speed controller should be added to overcome this problem. However, conventional controllers have not been successful for real time applications because of the change of reference and multiple input multiple output and time variant parameters. Predictive techniques are best suited for these situations. Model predictive control (MPC) is emerging as a powerful control scheme for high performance control of induction motor (IM) drives due to its fast speed response. This thesis presents finite set models predictive speed control of indirect vector controlled for a three-phase induction motor. The principle of vector control of electrical drives is based on the control of both the magnitude and the phase of each phase current and voltage. Indirect vector control to produce high performance in induction Motor drives by decoupling rotor flux and torque producing current components of stator current. The proposed system, complete mathematical model of vector controlled induction motor with model predictive controller is described and simulate in MATLAB for electrical vehicle system using squirrel cage type induction motor. This paper explores that the finite set model predictive control technique tracks the reference speeds with in 0.01sec and gives better performance than the proportional integral (PI) speed controller. The results proved that the induction motor with the finite set model predictive speed controller has superior transient response, and good robustness in face of uncertainties including reference speed changes and load disturbance. Moreover, accurate tracking performance has been achieved. Keywords: AC Drives, Induction Motor, Model Predictive Control, Speed Sensorless, Vector Controlled.