Noncentrosymmetric MoS2 semiconductors (1H, 3R) possess not only novel electronic structures of spin-orbit coupling (SOC) and valley polarization but also remarkable nonlinear optical effects. A more interesting noncentrosymmetric structure, the so-called 1T"'-MoS2 layers, was predicted to be built up from [MoS6] octahedral motifs by theoreticians, but the bulk 1T'''-MoS2 or its single crystal structure has not been reported yet. Here, we have successfully harvested 1T"' MoS2 single crystals by a topochemical method. The new layered structure is determined from single-crystal X-ray diffraction. The crystal crystallizes in space group P3(1)m with a cell of a = b = 5.580(2) angstrom and c = 5.957(2) angstrom, which is a root 3a x root 3a superstructure of 1T MoS2 with corner-sharing Mo-3 triangular trimers observed by the STEM. 1T"' MoS2 is verified to be semiconducting and possesses a band gap of 0.65 eV, different from metallic nature of IT or IT' MoS2. More surprisingly, the 1T"' MoS2 does show strong optical second-harmonic generation signals. This work provides the first layered noncentrosymmetric semiconductor of edge-sharing MoS6 octahedra for the research of nonlinear optics.