Infrared small target detection technology has sufficient applications in many engineering fields, such as infrared early warning, infrared tracking, and infrared reconnaissance. Due to the tiny size of the infrared small target and the lack of shape and texture information, existing methods often leave residuals or miss the target. To address these issues, a novel method based on a non-overlapping patch (NOP) joint l(0)-l(1) norm is proposed with the introduction of sparsity regularized principal component pursuit (SRPCP). The NOP model makes the patch lighter in the first place, reducing time consumption. The adoption of the l(0) norm enhances the sparsity of the target, while the adoption of thel(1)norm enhances the robustness of the algorithm under clutter. As a smart optimization method, SRPCP solves the NOP model fittingly and achieves stable separation of low-rank and sparse components, thereby improving detection capacity while suppressing the background efficiently. The proposed method ultimately yielded favorable detection results. Adequate experiment results demonstrate that the proposed method is competitive in terms of background suppression and true target detection with respect to state-of-the-art methods. In addition, our method also reduces the computational time.