Doppler shift compensation (DSC) is a unique feature observed in certain species of echolocating bats and is hypothesized to be an adaptation to detecting fluttering insects. However, current research on DSC has primarily focused on bats that are not engaged in foraging activities. In this study, we investigated the DSC performance of the Pratt's roundleaf bat, Hipposideros pratti, which was trained to pursue insects in various motion states within a laboratory setting. Our study yielded three main results. First, H. pratti demonstrated highly precise DSC during insect pursuit, aligning with previous findings of other flutter-detecting foragers during orientation or landing tasks. Second, we found that the motion state of the insect prey had little effect on the DSC performance of H. pratti. Lastly, we observed variations in H. pratti's DSC performance throughout the course of insect pursuit. The bats exhibited the highest DSC performance during the phase of maximum flight speed but declined performance during the phase of insect capture. These findings of high precision overall and of the time-dependent performance of DSC during insect pursuit support the hypothesis that DSC is an adaptation to detecting fluttering insects.