Infrared small target detection is widely used for early warning, aircraft monitoring, ship monitoring, and so on, which requires the small target and its background to be represented and modeled effectively to achieve their complete separation. Low-rank sparse decomposition based on the structural features of infrared images has attracted much attention among many algorithms because of its good interpretability. Based on our study, we found some shortcomings in existing baseline methods, such as redundancy of constructing tensors and fixed compromising factors. A self-adaptive low-rank sparse tensor decomposition model for infrared dim small target detection is proposed in this paper. In this model, the entropy of image block is used for fast matching of non-local similar blocks to construct a better sparse tensor for small targets. An adaptive strategy of low-rank sparse tensor decomposition is proposed for different background environments, which adaptively determines the weight coefficient to achieve effective separation of background and small targets in different background environments. Tensor robust principal component analysis (TRPCA) was applied to achieve low-rank sparse tensor decomposition to reconstruct small targets and their backgrounds separately. Sufficient experiments on the various types data sets show that the proposed method is competitive.