Theoretically, autism should be underpinned by aberrant brain dynamics. However, how brain activity changes over time in individuals with autism spectrum disorder (ASD) remains unknown. Here we characterize brain dynamics in autism using an energy-landscape analysis applied to resting-state fMRI data. Whereas neurotypical brain activity frequently transits between two major brain states via an intermediate state, high-functioning adults with ASD show fewer neural transitions due to an unstable intermediate state, and these infrequent transitions predict the severity of autism. Moreover, in contrast to the controls whose IQ is correlated with the neural transition frequency, IQ scores of individuals with ASD are instead predicted by the stability of their brain dynamics. Finally, such brain-behaviour associations are related to functional segregation between brain networks. These findings suggest that atypical functional coordination in the brains of adults with ASD underpins overly stable neural dynamics, which supports both their ASD symptoms and cognitive abilities.