Nipah virus (NiV) and related viruses form a distinct henipavirus genus within the Paramyxoviridae family. NiV continues to spillover into the humans causing deadly outbreaks with increasing human-bat interaction. NiV encodes the large protein (L) and phosphoprotein (P) to form the viral RNA polymerase machinery. Their sequences show limited homologies to those of non-henipavirus paramyxoviruses. We report two cryo-electron microscopy (cryo-EM) structures of the Nipah virus (NiV) polymerase L-P complex, expressed and purified in either its full-length or truncated form. The structures resolve the RNA-dependent RNA polymerase (RdRp) and polyribonucleotidyl transferase (PRNTase) domains of the L protein, as well as a tetrameric P protein bundle bound to the L-RdRp. L-protein C-terminal regions are unresolved, indicating flexibility. Two PRNTase domain zinc-binding sites, conserved in most Mononegavirales, are confirmed essential for NiV polymerase activity. The structures further reveal anchoring of the P protein bundle and P protein X domain (XD) linkers on L, via an interaction pattern distinct among Paramyxoviridae. These interactions facilitate binding of a P protein XD linker in the nucleotide entry channel and distinct positioning of other XD linkers. We show that the disruption of the L-P interactions reduces NiV polymerase activity. The reported structures should facilitate rational antiviral-drug discovery and provide a guide for the functional study of NiV polymerase.