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This paper proposes a new observer that computes the rotor speed of an induction motor by employing on-line a least-square algorithm implemented by an original neuron (total least squares (TLS) EXIN). It minimizes the estimation error from the equation of the Luenberger observer considering the rotor flux linkage estimation uncertainty. Experimental results show the goodness of this algorithm that outperforms the Matsuse observer in speed estimation accuracy at very low speed and zero-speed operations at no-load and at load. Moreover, it has been verified both numerically and experimentally that this observer works properly even at very low speeds in regenerating mode without any instability.