N6-methyladenosine (m6A) modification of mRNA is emerging as an important regulator of gene expression that affects different developmental and biological processes, and altered m6A homeostasis is linked to cancer1–5. m6A modification is catalysed by METTL3 and enriched in the 3′ untranslated region of a large subset of mRNAs at sites close to the stop codon5. METTL3 can promote translation but the mechanism and relevance of this process remain unknown1. Here we show that METTL3 enhances translation only when tethered to reporter mRNA at sites close to the stop codon, supporting a mechanism of mRNA looping for ribosome recycling and translational control. Electron microscopy reveals the topology of individual polyribosomes with single METTL3 foci in close proximity to 5′ cap-binding proteins. We identify a direct physical and functional interaction between METTL3 and the eukaryotic translation initiation factor 3 subunit h (eIF3h). METTL3 promotes translation of a large subset of oncogenic mRNAs—including bromodomain-containing protein 4—that is also m6A-modified in human primary lung tumours. The METTL3–eIF3h interaction is required for enhanced translation, formation of densely packed polyribosomes and oncogenic transformation. METTL3 depletion inhibits tumorigenicity and sensitizes lung cancer cells to BRD4 inhibition. These findings uncover a mechanism of translation control that is based on mRNA looping and identify METTL3–eIF3h as a potential therapeutic target for patients with cancer.