Time duration, an essential feature of the physical world, is perceived and cognitively interpreted subjectively. While this perception is deeply connected with arousal and interoceptive signals, the underlying neural mechanisms remain elusive. As the insula is critical for integrating information from the external world with the organism's inner state, we hypothesized that it might have a central role in the perception of time duration and contribute to its estimation accuracy. We conducted a functional magnetic resonance imaging study with 27 healthy participants performing temporal duration and pitch bisection tasks that used the same stimuli. By comparison with two referents with short and long duration in the time range of 1 s (close to the heart rate period), or low and high pitch, participants had to decide whether target stimuli were closer in duration or pitch to the referent stimuli. The temporal bisection point between short and long duration perception was obtained through a psychometric response curve analysis for each participant. The deviation between the bisection point and the average of reference stimuli durations was used as a marker of duration accuracy. Duration discrimination-specific activation, contrasted to pitch discrimination, was found in the dorsomedial prefrontal cortex, bilateral cerebellum, and right anterior insular cortex (AIC), extending to the inferior frontal gyrus (IFG), inferior parietal lobule, and frontal pole. The activity in the right AIC and IFG was positively correlated with the accuracy of duration discrimination. The right AIC is known to be related to the reproduction of duration, whereas the right IFG is involved in categorical decisions. Thus, the comparison between the referent durations reproduced in the AIC and the target duration may occur in the right IFG. We conclude that the right AIC and IFG contribute to the accurate perception of temporal duration.