Large language models (LLM) learn diverse knowledge present in the large-scale training dataset via self-supervised training. Followed by instruction-tuning, LLM acquires the ability to return correct information for diverse questions. However, adapting these pre-trained LLMs to new target domains, such as different organizations or periods, for the question-answering (QA) task incurs a substantial annotation cost. To tackle this challenge, we propose a novel task, unsupervised LLM adaptation for question answering. In this task, we leverage a pre-trained LLM, a publicly available QA dataset (source data), and unlabeled documents from the target domain. Our goal is to learn LLM that can answer questions about the target domain. We introduce one synthetic and two real datasets to evaluate models fine-tuned on the source and target data, and reveal intriguing insights; (i) fine-tuned models exhibit the ability to provide correct answers for questions about the target domain even though they do not see any questions about the information described in the unlabeled documents, but (ii) they have difficulties in accessing information located in the middle or at the end of documents, and (iii) this challenge can be partially mitigated by replacing input tokens with random ones during adaptation.