Essential tremor (ET) is a neurological disease with both motor and nonmotor manifestations; however, little is known about its underlying brain basis. Furthermore, the overall organization of the brain network in ET remains largely unexplored. We investigated the topological properties of brain functional network, derived from resting‐state functional magnetic resonance imaging (MRI) data, in 23 ET patients versus 23 healthy controls. Graph theory analysis was used to assess the functional network organization. At the global level, the functional network of ET patients was characterized by lower small‐worldness values than healthy controls—less clustered functionality of the brain. At the regional level, compared with the healthy controls, ET patients showed significantly higher values of global efficiency, cost and degree, and a shorter average path length in the left inferior frontal gyrus (pars opercularis), right inferior temporal gyrus (posterior division and temporo‐occipital part), right inferior lateral occipital cortex, left paracingulate, bilateral precuneus bilaterally, left lingual gyrus, right hippocampus, left amygdala, nucleus accumbens bilaterally, and left middle temporal gyrus (posterior part). In addition, ET patients showed significant higher local efficiency and clustering coefficient values in frontal medial cortex bilaterally, subcallosal cortex, posterior cingulate cortex, parahippocampal gyri bilaterally (posterior division), right lingual gyrus, right cerebellar flocculus, right postcentral gyrus, right inferior semilunar lobule of cerebellum and culmen of vermis. Finally, the right intracalcarine cortex and the left orbitofrontal cortex showed a shorter average path length in ET patients, while the left frontal operculum and the right planum polare showed a higher betweenness centrality in ET patients. In conclusion, the efficiency of the overall brain functional network in ET is disrupted. Further, our results support the concept that ET is a disorder that disrupts widespread brain regions, including those outside of the brain regions responsible for tremor.