Feature selection is one of the important topics of machine learning, and it has a wide range of applications in data preprocessing. At present, feature selection based on $\ell _{2,1}$-norm regularization is a relatively mature method, but it is not enough to maximize the sparsity and parameter-tuning leads to increased costs. Later scholars found that the $\ell _{2,0}$-norm constraint is more conductive to feature selection, but it is difficult to solve and lacks convergence guarantees. To address these problems, we creatively propose a novel Outliers Robust Unsupervised Feature Selection for structured sparse subspace (ORUFS), which utilizes $\ell _{2,0}$-norm constraint to learn a structured sparse subspace and avoid tuning the regularization parameter. Moreover, by adding binary weights, outliers are directly eliminated and the robustness of model is improved. More importantly, a Re-Weighted (RW) algorithm is exploited to solve our $\ell _{p}$-norm problem. For the NP-hard problem of $\ell _{2,0}$-norm constraint, we develop an effective iterative optimization algorithm with strict convergence guarantees and closed-form solution. Subsequently, we provide theoretical analysis about convergence and computational complexity. Experimental results on real-world datasets illustrate that our method is superior to the state-of-the-art methods in clustering and anomaly detection tasks.