The application of image steganography in popular image-sharing social networks requires robustness because the JPEG recompression in social networks changes the DCT coefficients of uploaded images. Currently, most robust steganography algorithms rely on the resistance of embedding to the general JPEG recompression process, while operations in a specific compression channel are usually ignored, which reduces the robustness performance. Besides, the state-of-the-art robust steganography needs to upload the cover image to social networks several times to acquire the robust cover image, which may be insecure in terms of behavior security. In this paper, a robust steganography method based on the softmax outputs of a trained classifier and protocol message embedding is proposed. In the proposed method, a deep learning-based robustness classifier is trained to model the specific process of the JPEG recompression channel. The prediction result of the classifier is used to select the robust DCT blocks to form the embedding domain. The selection information is embedded as the protocol messages into the middle-frequency coefficients of DCT blocks. To further improve the recovery possibility of the protocol message, a robustness enhancement method that decreases the predicted non-robust possibility of the robustness classifier by modifying low-frequency coefficients of DCT blocks is proposed. The experimental results show that the proposed method is universal and can be implemented in different JPEG compression channels after finetuning the classifier, and it has better robustness performance compared with state-of-the-art robust steganography and does not have the disadvantage in terms of behavior security, and it has better security performance compared with the state-of-the-art method when embedding large-sized secret messages.