The robust detection of small targets is one of the key techniques in infrared search and tracking applications. A novel small target detection method in a single infrared image is proposed in this paper. Initially, the traditional infrared image model is generalized to a new infrared patch-image model using local patch construction. Then, because of the non-local self-correlation property of the infrared background image, based on the new model small target detection is formulated as an optimization problem of recovering low-rank and sparse matrices, which is effectively solved using stable principle component pursuit. Finally, a simple adaptive segmentation method is used to segment the target image and the segmentation result can be refined by post-processing. Extensive synthetic and real data experiments show that under different clutter backgrounds the proposed method not only works more stably for different target sizes and signal-to-clutter ratio values, but also has better detection performance compared with conventional baseline methods.