The system parameters of induction motor (IM) vary significantly with different operating conditions. The temperature-dependent variation of the stator and rotor resistances, which induces a large estimation error on speed and flux, has been a critical issue for speed-sensorless control. To estimate simultaneous variations of the stator and rotor resistances in speed sensorless control of IMs under different operating conditions, an estimator is developed based on extended Kalman filter (EKF) technique. In order to resolve the instability issue of simultaneous estimation of stator and rotor resistances, the stator resistance is estimated via consideration of its temperature dependence and the thermal dynamics of the stator windings, whereas the rotor resistance is estimated as a constant state. Simulation results show that the EKF estimator, along with a controller developed based on the direct field-oriented control (DFOC) technique, achieves simultaneous estimation of the continuously changing resistances and maximum speed estimation error and speed control error of about 0.67%. The broken-bar phenomenon of rotor is also detected based on the rotor resistance estimation. Simulation results also display promising robustness to variation of system parameters, such as rotor and stator thermal time constants, which are not estimated by the proposed EKF algorithm.