Traditional multi-view clustering task is for complete data. However, in practical tasks, due to the limitation of the information acquisition method, some views tend to contain missing data, and this leads to the problem of incomplete multi-view clustering. In view of this problem, most of the existing clustering models are based on non-negative matrix factorization or distance graph, and their co-optimization strategy can easily make the performance of the solution insecure and the global structure can’t be fully characterized. In order to improve the performance of clustering graph, this paper proposed an incomplete multi-view clustering algorithm ALIMSC based on low-rank subspace clustering and anchor graph. The algorithm first obtained the benchmark similarity matrix of data by incomplete multi-view subspace clustering algorithm APMC based on anchor graph, which was embedded in the low-rank subspace clustering model. The similarity matrix was obtained by dimensionality ascending alignment and weighted fusion, and the final clustering graph was obtained by making the similarity matrix as consistent as possible with the benchmark similarity matrix. ALIMSC algorithm characterized the low-dimensional subspace distribution of high-dimensional data by imposing rank minimization constraint on the similarity matrix of each view and emphasized the subspace structure of the data on the basis of the original anchor graph, that is, the block diagonality reflected in the cluster graph. Experimental results on several public datasets show that the proposed algorithm outperforms the classical incomplete multi-view algorithms.