A novel coronavirus (COVID-19 virus) outbreak has caused a global pandemic resulting in tens of thousands of infections and thousands of deaths worldwide. The RNA-dependent RNA polymerase (RdRp, also named nsp12) is the central component of coronaviral replication/transcription machinery and appears to be a primary target for the antiviral drug, remdesivir. We report the cryo-EM structure of COVID-19 virus full-length nsp12 in complex with cofactors nsp7 and nsp8 at 2.9-Å resolution. In addition to the conserved architecture of the polymerase core of the viral polymerase family, nsp12 possesses a newly identified β-hairpin domain at its N terminus. A comparative analysis model shows how remdesivir binds to this polymerase. The structure provides a basis for the design of new antiviral therapeutics targeting viral RdRp.