Paramyxoviruses represent a family of RNA viruses causing significant human diseases. These include measles virus, the most infectious virus ever reported, in addition to parainfluenza virus, and other emerging viruses. Paramyxoviruses likely share common replication machinery but their mechanisms of RNA biosynthesis activities and details of their complex polymerase structures are unknown. Mechanistic and functional details of a paramyxovirus polymerase would have sweeping implications for understanding RNA virus replication and for the development of new antiviral medicines. To study paramyxovirus polymerase structure and function, we expressed an active recombinant Nipah virus (NiV) polymerase complex assembled from the multifunctional NiV L protein bound to its phosphoprotein cofactor. NiV is an emerging highly pathogenic virus that causes severe encephalitis and has been declared a global public health concern due to its high mortality rate. Using negative-stain electron microscopy, we demonstrated NiV polymerase forms ring-like particles resembling related RNA polymerases. We identified conserved sequence elements driving recognition of the 3'-terminal genomic promoter by NiV polymerase, and leading to initiation of RNA synthesis, primer extension, and transition to elongation mode. Polyadenylation resulting from NiV polymerase stuttering provides a mechanistic basis for transcription termination. It also suggests a divergent adaptation in promoter recognition between pneumo- and paramyxoviruses. The lack of available antiviral therapy for NiV prompted us to identify the triphosphate forms of R1479 and GS-5734, two clinically relevant nucleotide analogs, as substrates and inhibitors of NiV polymerase activity by delayed chain termination. Overall, these findings provide low-resolution structural details and the mechanism of an RNA polymerase from a previously uncharacterized virus family. This work illustrates important functional differences yet remarkable similarities between the polymerases of nonsegmented negative-strand RNA viruses.