This paper presents an efficient decoding approach for end-to-end automatic speech recognition (E2E-ASR) with large language models (LLMs). Although shallow fusion is the most common approach to incorporate language models into E2E-ASR decoding, we face two practical problems with LLMs. (1) LLM inference is computationally costly. (2) There may be a vocabulary mismatch between the ASR model and the LLM. To resolve this mismatch, we need to retrain the ASR model and/or the LLM, which is at best time-consuming and in many cases not feasible. We propose "delayed fusion," which applies LLM scores to ASR hypotheses with a delay during decoding and enables easier use of pre-trained LLMs in ASR tasks. This method can reduce not only the number of hypotheses scored by the LLM but also the number of LLM inference calls. It also allows re-tokenizion of ASR hypotheses during decoding if ASR and LLM employ different tokenizations. We demonstrate that delayed fusion provides improved decoding speed and accuracy compared to shallow fusion and N-best rescoring using the LibriHeavy ASR corpus and three public LLMs, OpenLLaMA 3B & 7B and Mistral 7B.