We propose eXtensible Prompt (X-Prompt) for prompting a large language model (LLM) beyond natural language (NL). X-Prompt instructs an LLM with not only NL but also an extensible vocabulary of imaginary words. Registering new imaginary words allows us to instruct the LLM to comprehend concepts that are difficult to describe with NL words, thereby making a prompt more descriptive. Also, these imaginary words are designed to be out-of-distribution (OOD) robust so that they can be (re)used like NL words in various prompts, distinguishing X-Prompt from soft prompt that is for fitting in-distribution data. We propose context-augmented learning (CAL) to learn imaginary words for general usability, enabling them to work properly in OOD (unseen) prompts. We experiment X-Prompt for zero-shot language style customization as a case study. The promising results of X-Prompt demonstrate its potential to facilitate advanced interaction beyond the natural language interface, bridging the communication gap between humans and LLMs.