Sparse unmixing plays an important role in hyperspectral image analysis due to its ability to sparsely estimate abundances with a potentially large-scale spectral library. However, most of the current unmixing techniques tend to run into bottlenecks due to their tendency to oversimplify the optimization problem by incorporating convex regularizations, which may not adequately address the intricacies present in complex data representations. To address this problem, we propose a nonconvex sparse unmixing method by employing a tensor low-rankness penalty, named NSUTLR. Specifically, the proposed NSUTLR considers ℓ1/2 regularization to enhance the sparsity of abundances, which further couples with the row-sparsity-promoting iterative weights. Besides, the proposed NSUTLR characterizes the low-rank property by applying a nonconvex tensor nuclear norm based on the log-sum of singular values. The proposed NSUTLR can be solved by applying the alternating direction method of the multiplier framework. Experiment results obtained from the proposed NSUTLR and competitors conducted on simulated and real hyperspectral images demonstrate the superior effectiveness of our proposed method.