In order to solve the problem of over-sparsity for within-class coefficients and over-density for between-class coefficients in SSC and LSR, this paper proposes a new subspace clustering based on Euclidean distance using A₂ norm. Using the weighted method based on Euclidean distance, the coefficient representation obtained by this algorithm maintains the connections of the data points from the same subspace. Meanwhile, the algorithm can eliminate the connections between clusters. The clusters can be produced by using the spectral clustering with the similarity matrix which is constructed by this coefficient representation. The results of experiments indicate the presented method improves the accuracy of clustering.