Despite considerable recent interest, the biological basis and clinical diagnosis of behavioural variant frontotemporal dementia (bvFTD) pose unresolved problems. Mentalising (the cognitive capacity to interpret the behaviour of oneself and others in terms of mental states) is impaired as a prominent feature of bvFTD, consistent with involvement of brain regions including ventro-medial prefrontal cortex (PFC), orbitofrontal cortex and anterior temporal lobes. Here, we investigated mentalising ability in a cohort of patients with bvFTD using a novel modality: music. We constructed a novel neuropsychological battery requiring attribution of affective mental or non-mental associations to musical stimuli. Mentalising performance of patients with bvFTD (n = 20) was assessed in relation to matched healthy control subjects (n = 20); patients also had a comprehensive assessment of behaviour and general neuropsychological functions. Neuroanatomical correlates of performance on the experimental tasks were investigated using voxel-based morphometry of patients' brain magnetic resonance imaging (MRI) scans. Compared to healthy control subjects, patients showed impaired ability to attribute mental states but not non-mental characteristics to music, and this deficit correlated with performance on a standard test of social inference and with carer ratings of patients' empathic capacity, but not with other potentially relevant measures of general neuropsychological function. Mentalising performance in the bvFTD group was associated with grey matter changes in anterior temporal lobe and ventro-medial PFC. These findings suggest that music can represent surrogate mental states and the ability to construct such mental representations is impaired in bvFTD, with potential implications for our understanding of the biology of bvFTD and human social cognition more broadly.