The supply-side current of an inverter-fed induction motor (IM) is easily accessible and less affected by noises than the motor stator current. This paper proposes a novel sensorless speed estimation method for an IM using the spectrum of the supply-side current. However, due to the influence of fundamental supply frequency, it is difficult to carry out the speed detection straight from the supply-side current signal. In this paper, an analytic model for characterizing the supply-side current of an inverter-fed IM using the modulation theory and the switching function concept is developed. Then, the Hilbert transform is applied to extract the speed harmonic component from the supply-side current. Finally, an interpolated Goertzel algorithm is put forward to enhance the estimation precision of IM speed. The performance of the proposed sensorless speed estimation method is proved by the speed estimation results obtained from hardware experiments of an IM fed by an inverter under different load conditions.