Low-rank and sparse decomposition method (LRSD) has been widely concerned in the field of infrared small target detection because of its good detection performance. However, existing LRSD-based methods still face the problems of low detection performance and slow detection speed in complex scenes. Although existing low-rank Tuck decomposition methods have achieved satisfactory detection performance in complex scenes, they need to define ranks in advance according to experience, and estimating the ranks too large or too small will lead to missed detection or false alarms. Meanwhile, the size of rank is different in different scenes. This means that they are not suitable for real-world scenes. To solve this problem, this paper uses non-convex rank approach norm to constrain latent factors of low-rank Tucker decomposition, which avoids setting ranks in advance according to experience and improves the robustness of the algorithm in different scenes. Meanwhile, a symmetric GaussSeidel (sGS) based alternating direction method of multipliers algorithm (sGSADMM) is designed to solve the proposed method. Different from ADMM, the sGSADMM algorithm can use more structural information to obtain higher accuracy. Extensive experiment results show that the proposed method is superior to the other advanced algorithms in detection performance and background suppression.