Adaptive inverse controllers (AIC) are based on approximate inverse of the system. This approximate inverse system is estimated using-some suitable estimators. They are incorporated in the feed forward path of the plant such that output of the plant tracks some desired signal. In AIC structure finite impulse response filters are used to compensate the effect of the non-cancellable zeros on the output, which avoid the cancellation of unstable poles of the controller with the non-cancellable zeros of the plant. So the boundedness of the input and output signals is assured. In practice the parameters of the controllers change as the frequency components of the reference input signal are changing. This means the parameters of the approximate inverse system designed using AIC method depend on the frequency spectrum of the excitation signal. This property results in highly time variant controller, where the frequency spectrum of the reference signal is not constant with time. In this work, a feed forward NN based structure of the AIC is proposed using the multi layer perceptrons (MLP). Back propagation algorithm is used as the learning algorithm for NN. The proposed structure shows the ability to control non-minimum phase system as well. It has been observed that once NN approximate inverse is learned, it becomes less sensitive to the frequency spectrum of excitation signal. Simulation results for both minimum phase and non-minimum phase plants are presented in the paper.