Summary: In this paper, we introduce the robust \(L_q\) \((0<q<1)\) regularization model, and then prove the global asymptotic distribution theorem for solutions of the model we propose. Applying the results, we can derive the model based on \(L_q\) \((0<q<1)\) regularization satisfying the consistent property of variable selection; in other words, it has the capacity of variable selection. To solve this model, we develop an iterative weighted algorithm without extra parameters, and give the corresponding strategy of selecting regularization parameters. The experiment results reveal that the algorithm we introduce is available, efficient and widely valuable.