The abnormal brain functional connectivity (FC) of patients with mental diseases is closely linked to the transition features among brain states. However, the current research on state transition will produce certain division deviations in the measurement method of state division, and also ignore the transition features among multiple states that contain more abundant information for analyzing brain diseases. To investigate the potential of the proposed method based on coarse-grained similarity measurement to solve the problem of state division, and consider the transition features among multiple states to analyze the FC abnormalities of autism spectrum disorder (ASD) patients. We used resting-state functional magnetic resonance imaging to examine 45 ASD and 47 healthy controls (HC). The FC between brain regions was calculated by the sliding window and correlation algorithm, and a novel coarse-grained similarity measure method was used to cluster the FC networks into five states, and then extract the features both of the state itself and the transition features among multiple states for analysis and diagnosis. (1) The state as divided by the coarse-grained measurement method improves the diagnostic performance of individuals with ASD compared with previous methods. (2) The transition features among multiple states can provide complementary information to the features of the state itself in the ASD analysis and diagnosis. (3) ASD individuals have different brain state transitions than HC. Specifically, the abnormalities in intra- and inter-network connectivity of ASD patients mainly occur in the default mode network, the visual network, and the cerebellum. Such results demonstrate that our approach with new measurements and new features is effective and promising in brain state analysis and ASD diagnosis.