The shallow models and linear functions are usually utilized for data embedding in data representation learning aimed at multi-view clustering. This strategy, however, cannot effectively mine the rich data relationships among the multiple views. For better representation of the consistency and complementarity information among different views, a tensor graph convolution network for multi-view clustering (TGCNMC) is proposed in this study. This method splices the traditional plane graphs into tensor graphs and uses tensor graph convolution to learn the neighbor relationships of the data in each view. Then, inter-graph convolution is adopted to transfer information among multiple views and thereby to capture the synergistic effect among the data of multiple views and reveal the consistency and complementarity information in those data. Finally, the self-monitoring method is employed for data clustering. Extensive experiments are carried out on standard data sets and the corresponding clustering results are better than those of the existing methods, which indicates that this method can represent multi-view data comprehensively, mine the relationships among views effectively, and deal with downstream clustering tasks beneficially.