A new series of triangular-lattice magnets, Na2BaMV 2O8 (M = Ni, Co, and Mn), are reported. These three compounds crystallize with the Ag2BaMnV2O8 type structure, where the magnetic M2+ ions form a two-dimensional triangular lattice. The magnitude of the exchange interactions in these compounds is moderate because the nonmagnetic VO4 tetrahedra interrupt direct connections between MO6 octahedra. The magnetic susceptibilities of Na2BaNiV2O8 and Na 2BaCoV2O8 reveal ferromagnetic transitions at 8.4 and 3.9 K, respectively. In contrast, the magnetic susceptibility of Na 2BaMnV2O8 exhibits a broad maximum at around 2.3 K, which suggests antiferromagnetic nearest-neighbour interactions and a significant effect of geometric frustration. The specific heat and magnetization curve of Na2BaMnV2O8 indicate that magnetic long-range ordering appears below 1.5 K.