A noncentrosymmetric crystal structure of CsCdBr3 has been successfully observed with X-ray single-crystal structure analysis. It crystallizes in the hexagonal space group P6(3)mc, with a 7.7281(14) Angstrom, b = 7.7281(14) Angstrom, c = 6.742(2) Angstrom, alpha = 90degrees, beta = 90degrees, gamma = 120degrees, Z = 2. It was obtained by a new preparation procedure different from that reported in the literature that gave a centrosymmetric structure. The structure contains Cd-Br octahedrons, which are connected in a plane-sharing way to form one-dimensional long chains. Each octahedron is slightly distorted, as the three Cd-Br bond lengths are 2.774 Angstrom, while the other three Cd-Br bond lengths are 2.804 Angstrom. The distortion directions of all of the octahedrons are almost parallel and give rise to the accumulation of the microcosmic nonlinear optical (NLO) coefficient. The Kurtz powder technique shows that CsCdBr3 has a powder second harmonic generation of about 2 times as large as that of potassium dihydrogen phosphate (KDP). It shows excellent transparency in the visible and infrared regions. The thermal stability is also good. Therefore it may be utilized as a potential nonlinear optical crystal for the IR region.