Data security technology is of great significance for the effective use of high-resolution remote sensing (HRRS) images in GIS field. Integrity authentication technology is an important technology to ensure the security of HRRS images. Traditional authentication technologies perform binary level authentication of the data and cannot meet the authentication requirements for HRRS images, while perceptual hashing can achieve perceptual content-based authentication. Compared with traditional algorithms, the existing edge-feature-based perceptual hash algorithms have already achieved high tampering authentication accuracy for the authentication of HRRS images. However, because of the traditional feature extraction methods they adopt, they lack autonomous learning ability, and their robustness still exists and needs to be improved. In this paper, we propose an improved perceptual hash scheme based on deep learning (DL) for the authentication of HRRS images. The proposed method consists of a modified U-net model to extract robust feature and a principal component analysis (PCA)-based encoder to generate perceptual hash values for HRRS images. In the training stage, a training sample generation method combining artificial processing and Canny operator is proposed to generate robust edge features samples. Moreover, to improve the performance of the network, exponential linear unit (ELU) and batch normalization (BN) are applied to extract more robust and accurate edge feature. The experiments have shown that the proposed algorithm has almost 100% robustness to format conversion between TIFF and BMP, LSB watermark embedding and lossless compression. Compared with the existing algorithms, the robustness of the proposed algorithm to lossy compression has been improved, with an average increase of 10%. What is more, the algorithm has good sensitivity to detect local subtle tampering to meet the high-accuracy requirements of authentication for HRRS images.