RNA-binding proteins (RBPs) play a pivotal role in gene expression by modulating the stability of transcripts; however, the identification of degradation targets of RBPs remains difficult. Here, we identified 48 target mRNAs of human Pumilio 1 (PUM1), an evolutionally conserved RBP, by combined analysis of transcriptome-wide mRNA stabilities and the binding of mRNAs to PUM1. Here, we developed an approach to identify mRNA targets of Pumilio 1 (PUM1), an evolutionally conserved RBP. By combined analysis of transcriptome-wide mRNA stabilities and the binding of mRNAs to PUM1, we identified 48 mRNAs that both bound to PUM1 and exhibited PUM1-dependent degradation. Analysis of changes in the abundance of PUM1 and its targets in RNA-seq data indicated that DNA-damaging agents negatively regulated PUM1-mediated mRNA decay. Cells exposed to cisplatin had reduced PUM1 abundance and increased PCNA and UBE2A mRNAs, encoding proteins involved in DNA repair by translesion synthesis (TLS). Cells overexpressing PUM1 exhibited impaired DNA synthesis and TLS and increased sensitivity to the cytotoxic effect of cisplatin. Thus, our method identified targets of PUM1-mediated decay and revealed that cells respond to DNA damage by inhibiting PUM1-mediated mRNA decay to activate TLS.