In this paper, a neural network model reference adaptive system speed observer is designed, which can be used inspeed control of linear induction motors (LIMs). Dynamical equations of LIM have been considered accurate. In otherwords, the end effect and the electrical losses of the motor have been included in the motor equivalent circuit. Thenequations of the reference model and adaptive model have been extracted. Existence of the speed-dependent functionsin the reference model causes error in speed estimation. In order to reduce error, the reference model equations areupdated unlike the standard MRAS method. The adaptive model equations have also been discrete and they have beenrewritten so as to be represented by a linear neural network (ADALINE). On this basis, the so-called back propagationhas been used to compute online, in recursive form, the machine linear speed. Finally, the estimated speed is used formotor speed control. The simulations show the efficiency of the method.