We propose LLMA, an LLM accelerator to losslessly speed up Large Language Model (LLM) inference with references. LLMA is motivated by the observation that there are abundant identical text spans between the decoding result by an LLM and the reference that is available in many real world scenarios (e.g., retrieved documents). LLMA first selects a text span from the reference and copies its tokens to the decoder and then efficiently checks the tokens' appropriateness as the decoding result in parallel within one decoding step. The improved computational parallelism allows LLMA to achieve over 2x speed-up for LLMs with identical generation results as greedy decoding in many practical generation scenarios where significant overlap between in-context reference and outputs exists (e.g., search engines and multi-turn conversations).