We report on the superconductivity in ternary transition metal tellurides Ta₂Pd₃Te₅ and Nb₂Pd₃Te₅, which have a one-dimensional crystal structure. Single-crystalline and polycrystalline samples of Ta₂Pd₃Te₅ show nonmetallic electron conduction, while Ti or W doping results in metallic behavior with a bulk superconducting transition at 2–4 K. In contrast, the polycrystalline samples of Nb₂Pd₃Te₅, which are found to be isostructural to Ta₂Pd₃Te₅, show a bulk superconducting transition at 3.3 K. The crystal structure and physical properties of Ta₂Pd₃Te₅ and Nb₂Pd₃Te₅ are also discussed in comparison with a candidate excitonic insulator Ta₂NiSe₅.