In some applications of inverter-fed induction motor drive systems, a fast and smooth restarting of free-running motors may be required when their inverters are faced with short-term power interruptions. In this article, a novel restarting strategy is proposed, consisting of three steps. First, during the restarting process, the initial step requires the machine's speed estimation. To achieve this, a dc current injection-based method is used to estimate the rotor flux and subsequently the speed of the rotating machine. In this step, a filtering and a phase-locked loop are used to extract speed information. Next, to further improve the speed estimation accuracy, the speed-sensorless vector control with zero torque command is used. Finally, a full-order adaptive observer is utilized for speed estimation in the restored normal operation of the induction motor. Compared to existing/alternative methods, the proposed strategy much faster estimates the initial speed and is able to restore the normal smooth operation within 0.5 s. The effectiveness of the proposed method is demonstrated by simulation and experimental studies.