Information compression is widely regarded as a fundamental principle that applies to human language. Zipf's law of abbreviation and Menzerath–Altmann's law are two linguistic laws related to information compression and have been demonstrated in human language and other communication systems. Female choice and male-male competition in anurans (frogs and toads) depend heavily on vocal communication. However, it remains unclear whether the laws reflecting information compression apply to vocal communication in anurans. Hainan frilled treefrogs, Kurixalus hainanus, are suitable anuran species to test Zipf's law of abbreviation and Menzerathe–Altmann's law as male K. hainanus can emit either monosyllabic or multisyllabic calls with three types of notes (i.e. A, B and C notes). In the present study, we mathematically examined whether the vocalizations of K. hainanus conform to these laws. We found that the note type duration was positively correlated with its frequency of occurrence, which was the opposite finding to that predicted by Zipf's law of abbreviation. We also found that the note duration was negatively correlated with call size (the number of notes in a call), but only A notes exhibited patterns consistent with Menzerath–Altmann's law when analysed separately. These results may be caused by the different physical characteristics or different functions and selection pressures of different note types. Further linear mixed model analysis showed that the duration of A notes was significantly negatively correlated with note position in a call, which suggests that the conformity to Menzerath–Altmann's law in A note is caused by energetic or breathing constraints on vocal production. Lastly, we observed a negative correlation between internote interval duration and call size. Our findings support the existence of information compression in vocal communication systems in anurans, among other communication principles, and contribute to increasing our understanding of universal patterns in communication systems.