Congenital cleft lip and palate is one of the common deformities in the craniomaxillofacial region. The current study aimed to explore the perceptual pattern of cleft-related speech produced by Mandarin-speaking patients with repaired cleft palate using the task-based functional magnetic resonance imaging (task-fMRI) technique. Three blocks of speech stimuli, including hypernasal speech, the glottal stop, and typical speech, were played to 30 typical adult listeners with no history of cleft palate speech exploration. Using a randomized block design paradigm, the participants were instructed to assess the intelligibility of the stimuli. Simultaneously, fMRI data were collected. Brain activation was compared among the three types of speech stimuli. Results revealed that greater blood-oxygen-level-dependent (BOLD) responses to the cleft-related glottal stop than to typical speech were localized in the right fusiform gyrus and the left inferior occipital gyrus. The regions responding to the contrast between the glottal stop and cleft-related hypernasal speech were located in the right fusiform gyrus. More significant BOLD responses to hypernasal speech than to the glottal stop were localized in the left orbital part of the inferior frontal gyrus and middle temporal gyrus. More significant BOLD responses to typical speech than to the glottal stop were localized in the left inferior temporal gyrus, left superior temporal gyrus, left medial superior frontal gyrus, and right angular gyrus. Furthermore, there was no significant difference between hypernasal speech and typical speech. In conclusion, the typical listener would initiate different neural processes to perceive cleft-related speech. Our findings lay a foundation for exploring the perceptual pattern of patients with repaired cleft palate.