We propose an instruction-following audio comprehension model that leverages the dialogue continuation ability of large language models (LLMs). Instead of directly generating target captions in training data, the proposed method trains a model to produce responses as if the input caption triggered a dialogue. This dialogue continuation training mitigates the caption variation problem. Learning to continue a dialogue effectively captures the caption's meaning beyond its surface-level words. As a result, our model enables zero-shot instruction-following capability without multitask instruction tuning, even trained solely on audio captioning datasets. Experiments on AudioCaps, WavCaps, and Clotho datasets with AudioBench audio-scene question-answering tests demonstrate our model's ability to follow various unseen instructions.