A photonic crystal is an artificial material with a periodic optical refractive index. The band structure of photons can be tailored by adjusting the geometric parameters spatially. By properly designing the configuration, the photonic crystal can generate an optical forbidden band within the structure. To choose an appropriate geometric configuration that can generate a photonic band gap in the desired frequency range, traditionally, the band structure of such structure has been obtained by applying Floquet periodic boundary conditions and performing the eigen analysis calculation. However, a great amount of testing is required and consumes a great amount of time. In our study, the top view of the unit cell is converted to a binary bitmap and encoded to downgrade the bitmap for forming the input data of the artificial neural network. We adopted the finite element method to calculate the band structure training data set, which contained various geometric parameters and corresponding band structures. Our neural network shows high accuracy and is less time-consuming. The results are useful for the inverse design of photonic crystals.