Abstract Background Depression in essential tremor (ET) has been constantly studied and reported, while the associated brain activity changes remain unclear. Recently, regional homogeneity (ReHo), a voxel-wise local functional connectivity (FC) analysis of resting-state functional magnetic resonance imaging, has provided a promising way to observe spontaneous brain activity. Methods Local FC analyses were performed in forty-one depressed ET patients, 49 non-depressed ET patients and 43 healthy controls (HCs), and then matrix FC and clinical depression severity correlation analyses were further performed to reveal spontaneous neural activity changes in depressed ET patients. Results Compared with the non-depressed ET patients, the depressed ET patients showed decreased ReHo in the bilateral cerebellum lobules IX, and increased ReHo in the bilateral anterior cingulate cortices and middle prefrontal cortices. Twenty-five significant changes of ReHo clusters were observed in the depressed ET patients compared with the HCs, and matrix FC analysis further revealed that inter-ROI FC differences were also observed in the frontal-cerebellar-anterior cingulate cortex pathway. Correlation analyses showed that clinical depression severity was positively correlated with the inter-ROI FC values between the anterior cingulate cortex and bilateral middle prefrontal cortices and was negatively correlated with the inter-ROI FC values of the anterior cingulate cortex and bilateral cerebellum lobules IX. Conclusion Our findings revealed local and inter-ROI FC differences in frontal-cerebellar-anterior cingulate cortex circuits in depressed ET patients, and among these regions, the cerebellum lobules IX, middle prefrontal cortices and anterior cingulate cortices could function as pathogenic structures underlying depression in ET patients.