Abstract: Phononic crystals represent a special kind of artificial periodic composite materials. The peculiar band-gap characteristics provide potential applications in the vibration reduction, wave filtering, sound insulation and acoustic functional devices. However, how to accurately manipulate acoustic and elastic waves is a major challenge for designing phononic crystals. The conventional design method is based on matching the specific application requirements by analyzing and adjusting the geometrical and material parameters of the phononic crystal structures. This method has a low efficiency and can hardly achieve the optimal performance. An artificial neural networks inverse design method for muti-layered phononic crystals based on the Softmax logistic regression and the multi-task learing is proposed in this study. In the proposed method, the Softmax logistic regression is used to choose the material type and the multi-task learing is used to determine the material distribution for each area of the multi-layered structure, so the phononic crystal reverse design problem is transformed into the classification problem of multi-component materials for the unit cell by the proposed method. First, a large number of the samples for the topological structures are randomly generated. Second, the band-gap structures of the samples are obtained by parallel finite element calculation. After that, the relationship between the topological structures and the band-gaps are established by the neural networks. Finally, the trained neural network is ultimately employed to design a phononic crystal structure with the targeted band-gaps, that is, the targeted band gap is used as the input of the neural network, and the trained neural network will output the corresponding cell topology of the phononic crystal unit cell directly. The example shows that the proposed method can obtain one-dimensional (1D) phononic crystals with the targeted band-gaps for the specified application requirements quickly and efficiently. This method provides a new way for the inverse design of phononic crystals.