Multi-view clustering is a kind of machine learning technique, with the potential to enhance the efficacy of clustering by integrating information from multiple sources. However, existing methods encounter limitations when dealing with multiview data, due to an inability to fully utilise the intrinsic correlation between the tensor low-rank representation and the affinity matrix, as well as under-performance in dealing with missing data, noise and outliers.To address these limitations, this paper proposes a multi-view sub-space clustering method based on tensor low-rank learning. The proposed method explores higher-order correlations between data points more thoroughly and accurately identifies the structure of the data by imposing low-rank constraints on data samples. Additionally, tensor singular value decomposition and weighted tensor kernel paradigm minimization method are employed to optimize the affinity matrix, transforming the clustering problem into a convex optimization problem to solve. This ensures the robustness and efficiency of the model. Furthermore, the method has been shown to effectively capture the intricate correlations present in multi-view data, thereby facilitating the identification of potential sub-space structures with greater precision. Extensive experimental evaluations have been conducted, using four distinct benchmark datasets, to assess the performance of the proposed method. The experimental results show that our method outperforms existing methods on four benchmark datasets, with high accuracy and robustness.