A new ternary manganese vanadate, NaMnVO4, was synthesized by solid state reaction route, and its crystal structure and magnetic properties were characterized by X-ray diffraction, magnetic susceptibility and specific heat measurements, and by density functional calculations. NaMnVO4 crystallizes in the maricite-type structure with space group Pnma, a = 9.563(1) angstrom, b = 6.882(1) angstrom, c = 5.316(1) angstrom, and Z = 4. NaMnVO4 contains MnO4 chains made up of edge-sharing MnO6 octahedra, and these chains are interlinked by VO4 tetrahedra. The magnetic susceptibility has a broad maximum at T-max = 24 K and follows the Curie Weiss behavior above 70 K with theta = -62 K. NaMnVO4 undergoes a three-dimensional antiferromagnetic ordering at T-N = 11.8 K. The spin exchanges of NaMnVO4 are dominated by the intrachain antiferromagnetic exchange, and the interchain spin exchanges are spin-frustrated. The most probable magnetic structure of the ordered magnetic state below T-N was predicted on the basis of the extracted spin exchanges.