Narrative comprehension is a challenging task that requires a deep understanding of the foundational elements of narratives. Acquiring this skill requires extensive annotated data. To mitigate the burden of data annotation, we present Parrot, a zero-shot approach for narrative reading comprehension through parallel reading, which involves two parallel narratives that tell the same story. By leveraging one narrative as a source of supervision signal to guide the understanding of the other, Parrot abstracts the textual content and develops genuine narrative understanding. Evaluation conducted on two narrative comprehension benchmarks demonstrates that Parrot surpasses previous zero-shot approaches and achieves comparable performance to fully supervised models. The code will be available at https://github.com/zhaochaocs/Parrot.