Cognitive flexibility (CF) is an executive function component related to the ability to flexibly shift amongst multiple incompatible perspectives or descriptions of an object task. However, whether CF enhances the narrative discourse comprehension of students with attention-deficit hyperactivity disorder (ADHD) during surface semantic meaning identification remains unclear. This study aimed to examine the impacts of CF on central word (CW) identification amongst primary school students with ADHD and reading comprehension difficulties (i.e. scores in the = 25th percentile of discourse comprehension but with adequate decoding skills and average decoding performance score within one standard deviation). In addition, the association of CF with CW identification performance, when the CW was located in either the first or second half of sentences, was tested with and without the interference of playing music. This study recruited 104 low-CF and 103 high-CF first grade students with ADHD and reading difficulties. Participants received measures of nonverbal intelligence, working memory, Chinese receptive vocabulary, Chinese word reading, CF and a music preference questionnaire. Additionally, participants completed the entire CW identification experiment (about 7 min) individually in a silent classroom located within the school campus. After controlling nonverbal intelligence, working memory, music preference, Chinese receptive vocabulary and Chinese word reading, the results showed that high-CF students had similar poetry discourse comprehension performance with low-CF students when the CWs were at the second half of a sentence. Moreover, high-CF students showed significantly better performance than low-CF students when the CWs were at the first half of the poetry sentences in both conditions with and without music, especially if the poetry sentence structure was more complicated than the typical 'subject-verb-object' sequence. All students with ADHD performed significantly worse in poetry discourse comprehension with music interference than without it. The results highlight the importance of CF in poetry discourse comprehension tasks, particularly when a poetry sentence uses a non-typical structure format. The possible effects of CF on poetry discourse comprehension are also discussed.