This paper is on realization of the speed-sensorless vector control of an induction motor using the RLS(Recursive Least Square) algorithm. The speed estimator is including the RLS algorithm and a rotor flux observer. The RLS algorithm has speed and rotor time constant as parameter vectors and rotor flux observer is designed to have robustness to stator resistance variation and through the IP(Integral and Proportional) speed controller stable performance is obtained for estimating rotor speed. Finally the total algorithm are realized in induction motor drive system and its effectiveness is verified.