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In recent years, many backdoor attacks based on training data poisoning have been proposed. However, in practice, those backdoor attacks are vulnerable to image compressions. When backdoor instances are compressed, the feature of specific backdoor trigger will be destroyed, which could result in the backdoor attack performance deteriorating. In this paper, we propose a compression-resistant backdoor attack based on feature consistency training. To the best of our knowledge, this is the first backdoor attack that is robust to image compressions. First, both backdoor images and their compressed versions are input into the deep neural network (DNN) for training. Then, the feature of each image is extracted by internal layers of the DNN. Next, the feature difference between backdoor images and their compressed versions are minimized. As a result, the DNN treats the feature of compressed images as the feature of backdoor images in feature space. After training, the backdoor attack against DNN is robust to image compression. Furthermore, we consider three different image compressions (i.e., JPEG, JPEG2000, WEBP) in feature consistency training, so that the backdoor attack is robust to multiple image compression algorithms. Experimental results demonstrate the effectiveness and robustness of the proposed backdoor attack. When the backdoor instances are compressed, the attack success rate of common backdoor attack is lower than 10%, while the attack success rate of our compression-resistant backdoor is greater than 97%. The compression-resistant attack is still robust even when the backdoor images are compressed with low compression quality. In addition, extensive experiments have demonstrated that, our compression-resistant backdoor attack has the generalization ability to resist image compression which is not used in the training process.