Artificial Neural Network (ANN) has achieved great success in many fields, such as image and voice recognition. Recently, ANN is also applied to solve inverse scattering problems, because of the advantages that it is able to produce estimation results in real time and without local minimum problems, compared to optimization techniques. However, in the problem of estimating the permittivity distribution of a layered medium from the information of incident and scattered waves, as the number of layers increases, the possible combinations of permittivity become enormous, making it difficult to train an ANN. On the other hand, the performance is not good enough when using ANN to recognize both the permittivity and thickness of each layer from the scattered wave information, because the scattered wave is affected by both of them. In this paper, we propose new data-preprocessing techniques to address these issues, and the ANN-based estimation obtained good accuracy even when the observed data include some noise.