Linguistic Steganography (LS) tasks aim to generate steganographic text (stego) based on secret information. Only authorized recipients can perceive the existence of secrets in the texts and extract them, thereby preserving privacy. However, the controllability of the stego generated by existing schemes is poor, and the stego is difficult to contain specific discourse characteristics such as style. As a result, the stego is easily detectable, compromising covert communication. To address these problems, this paper proposes LLsM, the first LS with the Large Language Model (LLM). We fine-tuned the LLaMA2 with a large-scale constructed dataset encompassing rich discourse characteristics, which enables the fine-tuned LLM to generate texts with specific discourse in a controllable manner. Then the discourse is used as guiding information and inputted into the fine-tuned LLM in the form of the Prompt together with secret. On this basis, the constructed candidate pool will be range encoded and use secret to determine the interval. The same prefix of this interval's beginning and ending is the secret embedded at this moment. Experiments show that LLsM performs superior to prevalent LS-task and related-task baselines regarding text quality, statistical analysis, discourse matching, and anti-steganalysis. In particular, LLsM's MAUVE matric surpasses some baselines by 70%-80%, and its anti-steganalysis performance is 30%-40% higher. Notably, we also present examples of longer stegos generated by LLsM, showing its potential superiority in long LS tasks.