Single-cell RNA sequencing (scRNA-seq) is a new technology that focuses on the expression levels for each cell to study cell heterogeneity. Thus, new computational methods matching scRNA-seq are designed to detect cell types among various cell groups. Herein, we propose a Multi-scale Tensor Graph Diffusion Clustering (MTGDC) for single-cell RNA sequencing data. It has the following mechanisms: 1) To mine potential similarity distributions among cells, we design a multi-scale affinity learning method to construct a fully connected graph between cells; 2) For each affinity matrix, we propose an efficient tensor graph diffusion learning framework to learn high-order information among multi-scale affinity matrices. First, the tensor graph is explicitly introduced to measure cell-cell edges with local high-order relationship information. To further preserve more global topology structure information in the tensor graph, MTGDC implicitly considers the propagation of information via a data diffusion process by designing a simple and efficient tensor graph diffusion update algorithm. 3) Finally, we mix together the multi-scale tensor graphs to obtain the fusion high-order affinity matrix and apply it to spectral clustering. Experiments and case studies showed that MTGDC had obvious advantages over the state-of-art algorithms in robustness, accuracy, visualization, and speed.