In order to explore the topological alterations in functional brain networks between multiple system atrophy (MSA) patients and healthy controls (HC), a new joint analysis method of static and dynamic functional connectivity (FC) is proposed in this paper. Twenty-four MSA patients and twenty HCs were enrolled in this study. We constructed static and dynamic brain networks from resting-state fMRI data and calculated four graph theory attributes. Statistical comparisons and correlation analysis were carried out for static and dynamic FC separately before combining both cases. We found decreased local efficiency (LE) and weighted degree (WD) in cerebellum from both static and dynamic graph attributes. For static FC alone, we identified increased betweenness centrality (BC) at left dorsolateral prefrontal cortex, left Cerebellum_Crus9 and decreased WD at Vermis_6. For dynamic FC alone, decreased BC, clustering coefficients and LE at several cortical regions and cerebellum were identified. All the features had significant correlation with total UMSARS scores. Receiver operating characteristic analysis showed that dynamic features had the highest area under the curve value. Our work not only added new evidence for the underlying neurobiology and disrupted dynamic disconnection syndrome of MSA, but also proved the possibility of disease diagnosis and progression tracking using rs-fMRI.