La-related protein 1 (LARP1) regulates the stability of many mRNAs. These include 5′TOPs, mTOR-kinase responsive mRNAs with pyrimidine-rich 5′ UTRs, which encode ribosomal proteins and translation factors. We determined that the highly conserved LARP1-specific C-terminal DM15 region of human LARP1 directly binds a 5′TOP sequence. The crystal structure of this DM15 region refined to 1.86 Å resolution has three structurally related and evolutionarily conserved helix-turn-helix modules within each monomer. These motifs resemble HEAT repeats, ubiquitous helical protein-binding structures, but their sequences are inconsistent with consensus sequences of known HEAT modules, suggesting this structure has been repurposed for RNA interactions. A putative mTORC1-recognition sequence sits within a flexible loop C-terminal to these repeats. We also present modelling of pyrimidine-rich single-stranded RNA onto the highly conserved surface of the DM15 region. These studies lay the foundation necessary for proceeding toward a structural mechanism by which LARP1 links mTOR signalling to ribosome biogenesis.