A new series of triangular-lattice magnets, Na(2)BaMV(2)O(8) (M = Ni, Co, and Mn), are reported. These three compounds crystallize with the Ag(2)BaMnV(2)O(8) type structure, where the magnetic M(2+) ions form a two-dimensional triangular lattice. The magnitude of the exchange interactions in these compounds is moderate because the nonmagnetic VO(4) tetrahedra interrupt direct connections between MO(6) octahedra. The magnetic susceptibilities of Na(2)BaNiV(2)O(8) and Na(2)BaCoV(2)O(8) reveal ferromagnetic transitions at 8.4 and 3.9 K, respectively. In contrast, the magnetic susceptibility of Na(2)BaMnV(2)O(8) 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 Na(2)BaMnV(2)O(8) indicate that magnetic long-range ordering appears below 1.5 K.