A new chalcogenide Na2ZnSnS4 has been successfully synthesized by using Na2S2 as reactive flux. Na2ZnSnS4 crystallizes in the tetragonal system with space group of I (4) over bar. Its cell parameters are a = 6.4835(6) angstrom and c = 9.134(1) angstrom. The structure is a derivative of AgGaS2, in which the Ag+ ions are replaced by Na+ ions and the Ga3+ ions are replaced by Zn2+ and Sn' ions. All three cations are in seriously distorted tetrahedral geometry with a distortion factor (eta = c/a) of 1.4. Optical measurements show that the Na2ZnSnS4 powder sample has a large transparent range from 0.8 to 25 ym and a wide band gap of 3.1 eV. It exhibits large second harmonic generation intensity of 0.9 x AgGaS2 in the grain size range from 41 to 74 ym. First-principles calculation results reveal that the valence band maximum and conduction band minimum are mainly composed of S 3p, Zn 3d orbitals and Sn Ss, S 3p orbitals, respectively.