The functional coupling of the cerebral cortex and muscle contraction indicates that electroencephalogram (EEG) and surface electromyogram (sEMG) signals are coherent. The objective of this study is to clearly describe the coupling relationship between EEG and sEMG through a variety of analysis methods. We collected the EEG and sEMG data of left- or right-hand motor imagery and motor execution from six healthy subjects and six stroke patients. To enhance the coherence coefficient between EEG and sEMG signals, the algorithm of EEG modification based on the peak position of sEMG signals is proposed. Through analyzing a variety of signal synchronization analysis methods, the most suitable coherence analysis algorithm is selected. In addition, the wavelet coherence analysis method based on time spectrum estimation was used to study the linear correlation characteristics of the frequency domain components of EEG and sEMG signals, which verified that wavelet coherence analysis can effectively describe the temporal variation characteristics of EEG–sEMG coherence. In the task of motor imagery, the significant EEG–sEMG coherence is mainly in the imagination process with the frequency distribution of the alpha and beta frequency bands; in the task of motor execution, the significant EEG–sEMG coherence mainly concentrates before and during the task with the frequency distribution of the alpha, beta, and gamma frequency bands. The results of this study may provide a theoretical basis for the cooperative working mode of neurorehabilitation training and introduce a new method for evaluating the functional state of neural rehabilitation movement.