Due to the efficiency of exploiting relationships and complex structures hidden in multi-views data, graph-oriented clustering methods have achieved remarkable progress in recent years. But most existing graph-based spectral methods still have the following demerits: (1) They regularize each view equally, which does not make sense in real applications. (2) By employing different norms, most existing methods calculate the error feature by feature, resulting in neglecting the spatial structure information and the complementary information. To tackle the aforementioned drawbacks, we propose an enhanced multi-view spectral clustering model. Our model characterizes the consistency among indicator matrices by minimizing our proposed weighted tensor nuclear norm, which explicitly exploits the salient different information between singular values of the matrix. Moreover, our model adaptively assigns a reasonable weight to each view, which helps improve robustness of the algorithm. Finally, the proposed tensor nuclear norm well exploits both high-order and complementary information, which helps mine the consistency between indicator matrices. Extensive experiments indicate the efficiency of our method.