A phononic crystal is an artificial material with spatially elastic modulus usually designed for sensing. By using Bloch’s theorem and the concept of the Brillouin zone, the phononic band structure can be obtained. The phononic crystal slab is formed by arranging two-dimensional periodic structures in an elastic slab. The periodic structure can control the propagation direction of the elastic wave, which is parallel to the slab and has great potential for many applications. However, it is time-consuming to determine the proper design. The artificial neural network is a promising tool for solving complex problems. We aim to train a neural network to predict the phononic band structure of silicon phononic crystal slabs. The training data are obtained by the finite element method. Our results show that the proposed artificial neural network can rapidly predict the eigenfrequencies of the band structure with high accuracy.