This paper proposes a novel robust speed control method for induction motor drives based on a two-layered neural network plant estimator (NNPE) and a two-layered neural network PI controller (NNPIC). The NNPE is used to provide a real-time adaptive estimation of the unknown motor dynamics. The widely used projection algorithm is used as the learning algorithm for these neural networks to automatically adjust the parameters of the NNPIC and to minimize the differences between the motor speed and the speed predicted by the NNPE. The simulation and experimental results demonstrate that the proposed robust control scheme can improve the performance of an induction motor drive and reduce its sensitivity to parameter variations and load disturbances.