To better explore the underlying intrinsic structure of tensorial data, in this Letter, the authors propose a low-rank approximation-based tensor decomposition (LRATD) algorithm for subspace clustering. LRATD aims to seek a low-dimensional intrinsic core tensor representation by projecting the original tensor into a subspace spanned by projection matrices. Different from traditional approaches that impose additional constraints on basis matrices to further eliminate the influence of data noise or corruption, they directly add a low-rank regulariser on the core tensor to encourage more robust feature representation. Noticeably, they develop an accelerated proximal gradient algorithm to solve the problem of LRATD. Experimental results demonstrate the excellent performance compared with state-of-the-art methods.