In response to the escalating demand for digital human representations, progress has been made in the generation of realistic human gestures from given speeches. Despite the remarkable achievements of recent research, the generation process frequently includes unintended, meaningless, or non-realistic gestures. To address this challenge, we propose a gesture translation paradigm, GesTran, which leverages large language models (LLMs) to deepen the understanding of the connection between speech and gesture and sequentially generates human gestures by interpreting gestures as a unique form of body language. The primary stage of the proposed framework employs a transformer-based auto-encoder network to encode human gestures into discrete symbols. Following this, the subsequent stage utilizes a pre-trained LLM to decipher the relationship between speech and gesture, translating the speech into gesture by interpreting the gesture as unique language tokens within the LLM. Our method has demonstrated state-of-the-art performance improvement through extensive and impartial experiments conducted on public TED and TED-Expressive datasets.