Music is widely used as an auxiliary treatment for the recovery of motor function and emotional regulation in patients with epilepsy, Parkinson’s disease, and stroke. It also has certain positive impacts on physiology and psychology during physical exercise. This study investigates the functional corticomuscular coupling (FCMC) relationship and the changes in the brain functional connection mode in normal people in response to music stimuli when the right hand continuously outputs grip power. Electroencephalography (EEG) and electromyography (EMG) tests are synchronously performed on normal participants with music stimuli, with audiobook stimuli, and without stimulation. The similarity, causality, and direction of the signals are calculated by EEG-EMG coherence and transfer entropy (TE), and the brain functional connectivity network is established to analyze the changes in the coupling relationship between regions of the brain and between different regions of the brain and muscles. It is found that, for the CP2, FC2, and four muscle channels in this study, music stimuli reduce EEG-EMG coherence. In addition, the characteristics of corticomuscular TE and the brain functional connectivity network with music stimuli are quite different from other groups. This paper explores the effects of music stimuli on FCMC from the perspective of physiological electrical signal analysis, which may have a positive impact on future studies of music therapy in neurorehabilitation.