A new multi-scale compensation transfer entropy (MeTE) method was proposed, in order to describe accurately the coupling characteristics between electroencephalogram (EEG) and electromyographic (EMG) signals at different scales. An adaptive-projection intrinsically transformed multivariate empirical mode decomposition method and the compensation transfer entropy were combined in the proposed method. The multi-scale compensation transfer entropy values at different scales were calculated, and calculation results were used to quantitatively analyze the coupling characteristics of different coupling directions. Results show that under constant grip strength, the coupling strength between the beta frequency band (13-35 Hz) is significant, and the coupling strength of the ${\text{EEG}} \to {\text{EMG}}$direction is higher than ${\text{EMG}} \to {\text{EEG}}$direction. In the high gamma frequency band (50-72 Hz), the coupling strength of EEG and EMG in ${\text{EEG}} \to {\text{EMG}}$direction is generally higher than that in ${\text{EMG}} \to {\text{EEG}}$direction. Research results reveal that the coupling intensity of EEG and EMG signals in different coupling directions and different scales is different. And the McTE can estimate accurately the coupling characteristics and functional connection between EEG and EMG signals at different scales are estimated accurately by using McTE method.