The coronavirus SARS-CoV-2 uses an RNA-dependent RNA polymerase (RdRp) for the replication of its genome and the transcription of its genes1–3. Here we present the cryo-electron microscopic structure of the SARS-CoV-2 RdRp in active form, mimicking the replicating enzyme. The structure comprises the viral proteins nsp12, nsp8, and nsp7, and over two turns of RNA template-product duplex. The active site cleft of nsp12 binds the first turn of RNA and mediates RdRp activity with conserved residues. Two copies of nsp8 bind to opposite sides of the cleft and position the second turn of RNA. Long helical extensions in nsp8 protrude along exiting RNA, forming positively charged ‘sliding poles’. These sliding poles can account for the known processivity of the RdRp that is required for replicating the long coronavirus genome3. Our results enable a detailed analysis of the inhibitory mechanisms that underlie the antiviral activity of substances such as remdesivir, a drug for the treatment of coronavirus disease 2019 (COVID-19)4.