In most sparse coding based subspace clustering problems, using the non-convex lp-norm minimization (0 < p < 1) can often deliver better results than using the convex l1-norm minimization. In this paper, we propose a sparse subspace clustering via joint lp-norm and l2,p-norm minimization, where the lp-norm imposed on sparse representations can achieve more sparsity for clustering while l2,p-norm imposed on reconstructed error can handle outlier pursuit. We also propose an iterative solution to solve the proposed problem based on Iterative Shrinkage/Thresholding (IST) method. In addition, to the best knowledge, utilizing IST for solving l2,p-norm minimization problem can be the first work in our paper and there is no such work before. Finally, to demonstrate the improved performance of the proposed method, comparative study was performed on benchmark problems of image clustering. Thoroughly experimental studies on real world datasets show that the method can significantly outperform other state-of-the-art methods.