Given the great success of large language models (LLMs) across various tasks, in this paper, we introduce LLM-ST, a novel and effective speech translation model constructed upon a pre-trained LLM. By integrating the large language model (LLM) with a speech encoder and employing multi-task instruction tuning, LLM-ST can produce accurate timestamped transcriptions and translations, even from long audio inputs. Furthermore, our findings indicate that the implementation of Chain-of-Thought (CoT) prompting can yield advantages in the context of LLM-ST. Through rigorous experimentation on English and Chinese datasets, we showcase the exceptional performance of LLM-ST, establishing a new benchmark in the field of speech translation. Demo: https://speechtranslation.github.io/llm-st/.