A single-frame on-axis digital hologram reconstruction method based on deep learning is proposed to suppress the zero-order and twin images in on-axis digital holography based on the powerful feature extraction capabilities. The U-Net is used to train and reconstruct different kinds on-axis holograms, including intensity and phase targets. The results show that the U-Net-based neural network can achieve high-precision reconstruction of the on-axis holograms. A set of on-axis holograms based on letters with different noise levels are generated to verify the robustness of the U-Net-based neural network. The results show that the U-Net-based neural network is robust to different targets and noise levels, and the structural similarity of the reconstruction results is better than 0.92.