This Letter aims to propose a dynamic-range compression and decompression scheme for digital holograms that uses a deep neural network (DNN). The proposed scheme uses simple thresholding to compress the dynamic range of holograms with 8-bit gradation to binary holograms. Although this can decrease the amount of data by one-eighth, the binarization strongly degrades the image quality of the reconstructed images. The proposed scheme uses a DNN to predict the original gradation holograms from the binary holograms, and the error-diffusion algorithm of the binarization process contributes significantly to training the DNN. The performance of the scheme exceeds that of modern compression techniques such as JPEG 2000 and high-efficiency video coding.