We propose a two-stage neural network method to maximize the bandgap of 2D photonic crystals. The proposed model consists of a fully connected deep feed-forward neural network (FNN) and U-Net, which are employed, respectively, to generate the shape function and learn the sensitivity. The shape is generated by the FNN during the entire optimization process, and obtaining the sensitivity can be split into two steps. In the first step of the optimization, the sensitivity is calculated by finite element analysis (FEA) and the result is used as a sample to train the U-Net. Second, the optimization procedure is adopted instead of FEA, where a trained U-Net is used to generate the corresponding sensitivity. The main advantage of such an approach is that the shape function and sensitivity can be obtained by neural networks without solving a partial differenital equation. Therefore, the computational cost can be reduced by the proposed method without using large training sets. The effectiveness of the proposed method is verified in the numerical experiments in terms of the optimized shape and time consumption.