Two new quaternary mixed metal oxide materials InVTe2O8 and InVSe2O8 have been synthesized, as crystals and pure bulk powders by standard solid-state reactions using In2O3, V2O5, and TeO2 (or SeO2) as reagents. The crystal structures of the reported materials were determined using single-crystal X-ray diffraction. InVTe2O8 crystallizes in the monoclinic centrosymmetric space group P2(1)/n (No. 14), with unit-cell parameters of a = 7.8967(16) angstrom, b = 5.1388(10) angstrom, c = 16.711(3) angstrom, beta = 94.22(3)degrees, and Z = 4, and InVSe2O8 crystallizes in the noncentrosymmetric space group Pm (No. 6) with unit-cell parameters of a = 4.6348(9) angstrom, b = 6.9111(14) angstrom, c = 10.507(2) angstrom, beta = 97.77(3)degrees, and Z = 2. While the centrosymmetric InVTe2O8 shows a two-dimensional (2D) layered structure composed of InO6 octahedra, VO4 tetrahedra, and TeO4 polyhedra, the noncentrosymmetric InVSe2O8 exhibits a three-dimensional (3D) framework structure with distorted InO6 octahedra, VO5 square pyramids, and SeO3 polyhedra. Powder second-harmonic generation (SHG) measurements on InVSe2O8, using 1064-nm radiation, indicate that the material has a SHG efficiency similar to 30 times that of alpha-SiO2. Additional SHG measurements reveal that the material is not phase-matchable (Type 1). Infrared, ultraviolet visible light (UV-vis) diffuse reflectance, and thermogravimetric analyses for the two compounds are also presented, as are dipole moment calculations.