Replication-dependent histone (RDH) mRNAs have a nonpolyadenylated 3-UTR that ends in a highly conserved stem-loop structure. Nonetheless, a subset of RDH mRNAs has a poly(A) tail under physiological conditions. The biological meaning of poly(A)-containing (+) RDH mRNAs and details of their biosynthesis remain elusive. Here, using HeLa cells and Western blotting, qRT-PCR, and biotinylated RNA pulldown assays, we show that poly(A)(+) RDH mRNAs are post-transcriptionally regulated via adenylate- and uridylate-rich element-mediated mRNA decay (AMD). We observed that the rapid degradation of poly(A)(+) RDH mRNA is driven by butyrate response factor 1 (BRF1; also known as ZFP36 ring finger protein-like 1) under normal conditions. Conversely, cellular stresses such as UV C irradiation promoted BRF1 degradation, increased the association of Hu antigen R (HuR; also known as ELAV-like RNA-binding protein 1) with the 3-UTR of poly(A)(+) RDH mRNAs, and eventually stabilized the poly(A)(+) RDH mRNAs. Collectively, our results provide evidence that AMD surveils poly(A)(+) RDH mRNAs via BRF1-mediated degradation under physiological conditions.