Sensorless speed estimation in induction motor systems is one of the most control engineers. Based on the estimated speed the vector control has been applied to the high precision torque control however most speed estimation methods use adaptive scheme so that it takes long time to estimate the speed. Thus the adaptive estimation scheme is not effective to the induction motor which requires short sampling time. In this paper a new linearized equation of induction motor system is proposed and a sensorless speed estimation algorithm based on observation techniques is developed. First the nonlinear induction motor equation is linearized at an equilibrium point. Second a proportional integral(PI) observer is applied to estimate the speed state in the induction motor system. Finally simulation results will assure the effectiveness of the new linearized equation and the sensorless estimation algorithm by using PI observer in the nonlinear induction motor system.