Single crystals of a novel Na-Pt-Si ternary compound, Na3Pt10Si5, were synthesized by heating the constituent elements at 1423 K. It crystallizes in a non-centrosymmetric trigonal structure of space group R32 (Z = 3) with lattice constants of a = 10.1536(3) Å and c = 10.1539(3) Å at 300 K. The structure consists of a three-dimensional framework made of Pt and Si atoms, and the Na atoms are contained in the tunnels of the framework. The large magnitude and the temperature dependence of the atomic displacement parameter of the Na site reveal a large thermal vibration indicative of a "rattling" motion of Na atoms in the oversized tunnel. The electronic structure calculations explain the observed metallic properties on the basis of the covalent bonds between the Pt and Si atoms in the framework and the ionic bonding of the Na atoms to the framework. A type II superconductivity with a transition temperature of 2.9 K and an upper critical field of 2.5 kOe are observed for a polycrystalline sintered bulk sample of Na3Pt10Si5 prepared by heating at 1353 K in Na vapor. Heat capacity measurements reveal a strong coupling superconductivity that is probably caused by an electron-phonon interaction enhanced by the rattling motion of the Na atoms.