Summary: Incomplete multiview clustering (IMVC) has attracted extensive attention in the field of machine learning due to its excellent performance in handling incomplete multiview data (IMVD). However, existing IMVC methods often use spectral clustering or k-means on the obtained affinity matrices to obtain the final clustering results, that is, the affinity matrices learning process and clustering process are separated. In this paper, we propose a new ingenious IMVC method, one-step incomplete multiview clustering with low-rank tensor graph learning (OIMVC/LTGL), to solve the problem. This method combines graph learning, low-rank tensor constraint, common representation learning and clustering into a unified optimization framework. First, we utilize the adjacency relationship between views to complete the similarity graph matrices. Second, we stack all similarity graph matrices into a third-order tensor. To mine higher-order correlations among different views, we impose a low-rank tensor constraint, the tensor nuclear norm (TNN), into the constructed tensor. Third, to explore consistent information between views, we introduce a common representation learning term to learn the optimal consensus representation. Last, we introduce spectral rotation to the consensus representation matrices to directly obtain the clustering labels. These steps promote each other for better clustering performance. We solve the optimization problem by using the augmented Lagrange multiplier (ALM) method. Experiments based on five well-known datasets show the superiority of our method.