Music is inherent in human life and is a significant topic of cognitive neuroscience. Previous studies focused on amusia suggested that two frontotemporal circuits engage in music processing. Structure-function coupling is an important feature of human brain, which is associated with cognition and allows for a more sensitive investigation of brain-behavior association. However, we still have limited knowledge about the relation between structure-function coupling, music processing and other regional neural profiles. We recruited 106 participants (43 subjects were diagnosed with congenital amusia) and measured their music perception by Montreal Battery of Evaluation of Amusia (MBEA). Then we utilized support vector regression algorithm and mediation analysis, and employed amplitude of low frequency fluctuation (ALFF), structural/functional degree centrality (DC) and structure-function coupling to explore their relation with global averaged MBEA score. We found structure-function coupling of widespread brain regions in both hemispheres, rather than ALFF or DC, contributed to predict MBEA score. Left middle frontal gyrus, bilateral inferior temporal gyrus and right insula were most predictive regions, and these regions were involved in memory and cognitive control according to meta-analysis. Further, coupling of left middle frontal gyrus, a region that is homologous to and is connected with typical music circuits, fully mediated the negative relation between ALFF and MBEA score. Our findings provide further understanding for the neural basis of music, and have implications for neural plasticity, neuromodulation therapy and cognitive causes of amusia.