Hyperspectral anomaly detection (HAD) has attracted extensive interests because of its broad applications in both military and civilian. In recent years, morphological-attribute-filter based method has been applied to the HAD task achieving impressive performances. How-ever, how to introduce morphological attribute filters into convex-optimization-based HAD models is still an unsolved problem. In this paper, for the first time, we designed a morphological attribute filter-based regularizer to assist the low-rank representation model in utilizing morphological spatial structure information. The newly proposed model is called as background-suppression regularized low-rank representation (BSLRR). Furthermore, we design a customized automatic dictionary construction scheme for facilitating the practical applicability of BSLRR. Experiments show that BSLRR has certain advantages over benchmark methods.