The angular gyrus (AG) is a hub of several networks that are involved in various functions, including attention, self-processing, semantic information processing, emotion regulation, and mentalizing. Since these functions are required in music performance, it is likely that the AG plays a role in music performance. Considering that these functions emerge as network properties, this study analyzed the functional connectivity of the AG during the imagined music performance task and the resting condition. Our hypothesis was that the functional connectivity of the AG is modulated by imagined music performance. In the resting condition, the AG had connections with the medial prefrontal cortex (mPFC), posterior cingulate cortex (PCC), and precuneus as well as the superior and inferior frontal gyri and with the temporal cortex. Compared with the resting condition, imagined music performance increased the functional connectivity of the AG with the superior frontal gyrus (SFG), mPFC, precuneus, PCC, hippocampal/parahippocampal gyrus (H/PHG), and amygdala. The anterior cingulate cortex (ACC) and superior temporal gyrus (STG) were newly engaged or added to the AG network during the task. In contrast, the supplementary motor area (SMA), sensorimotor areas, and occipital regions, which were anti-correlated with the AG in the resting condition, were disengaged during the task. These results lead to the conclusion that the functional connectivity of the AG is modulated by imagined music performance, which suggests that the AG plays a role in imagined music performance.