Sleep is an essential integrant in everyone’s daily life; therefore, it is an important but challenging problem to characterize sleep stages from electroencephalogram (EEG) signals. The network motif has been developed as a useful tool to investigate complex networks. In this study, we developed a multiplex visibility graph motif-based convolutional neural network (CNN) for characterizing sleep stages using EEG signals and then introduced the multiplex motif entropy as the quantitative index to distinguish the six sleep stages. The independent samples t-test shows that the multiplex motif entropy values have significant differences among the six sleep stages. Furthermore, we developed a CNN model and employed the multiplex motif sequence as the input of the model to classify the six sleep stages. Notably, the classification accuracy of the six-state stage detection was 85.27%. Results demonstrated the effectiveness of the multiplex motif in characterizing the dynamic features underlying different sleep stages, whereby they further provide an essential strategy for future sleep-stage detection research.