This paper proposes a speed-sensorless induction motor control system using a rotor speed compensation. To explain the proposed system, this paper describes an induction motor model in the synchronous reference frame for the vector control. The rotor flux is estimated by the rotor flux observer using the reduced-dimensional state estimator technique. The estimated rotor speed is directly obtained from the electrical frequency, the slip frequency, and the rotor speed compensation with the estimated q-axis rotor flux. The error of the rotor time constant is indirectly reflected in the rotor speed compensation using the compensation of the flux error angle. To precisely estimate the rotor flux, the actual value of the stator resistance, whose actual variation is reflected, is derived. An implementation of pulse-width modulation (PWM) pulses using an effective space vector modulation (SVM) is briefly mentioned. For fast calculation and improved performance of the proposed algorithm, all control functions are implemented in software using a digital signal processor (DSP) with its environmental circuits. Also, it is shown through experimental results that the proposed system gives good performance for the speed-sensorless induction motor control.