Influenza virus mRNA is stable and competent for nuclear export and translation because it receives a 5′ cap(1) structure in a process called cap-snatching1. During cap-snatching, the viral RNA-dependent RNA polymerase (FluPol) binds to host RNA polymerase II (Pol II) and the emerging transcript2,3. The FluPol endonuclease then cleaves a capped RNA fragment that sub-sequently acts as a primer for the transcription of viral genes4,5. Here, we present the cryo-EM structure of FluPol bound to a transcribing Pol II in complex with the elongation factor DSIF in the pre-cleavage state. The structure shows that FluPol directly interacts with both Pol II and DSIF, which position the FluPol endonuclease domain near the RNA exit channel of Pol II. These interactions are important for the endonuclease activity of FluPol and FluPol activity in cells. A second structure trapped after cap-snatching shows that cleavage rearranges the capped RNA primer within the FluPol, directing the capped RNA 3′-end towards the FluPol polymerase active site for viral transcription initiation. Altogether, our results provide the molecular mechanisms of co-transcriptional cap-snatching by FluPol.