Background modeling is a critical component for various vision-based applications. Most traditional methods tend to be inefficient when solving large-scale problems. In this paper, we introduce sparse representation into the task of large-scale stable-background modeling, and reduce the video size by exploring its discriminative frames. A cyclic iteration process is then proposed to extract the background from the discriminative frame set. The two parts combine to form our sparse outlier iterative removal (SOIR) algorithm. The algorithm operates in tensor space to obey the natural data structure of videos. Experimental results show that a few discriminative frames determine the performance of the background extraction. Furthermore, SOIR can achieve high accuracy and high speed simultaneously when dealing with real video sequences. Thus, SOIR has an advantage in solving large-scale tasks.