Two new quaternary vanadium selenite and tellurite, i.e., YVSe2O8 and YVTe2O8, have been synthesized through hydrothermal and solid-state reactions. Both of the reported materials exhibit three-dimensional framework structures that are composed of layers of corner-shared VO6 octahedra, layers of edge-shared YO8 groups, and SeO3 or TeO3 linkers. While YVSe2O8 crystallizes in the orthorhombic noncentrosymmetric (NCS) space group, Abm2, YVTe2O8 reveals the monoclinic centrosymmetric (CS) space group, C2/m. The band gaps for YVSe2O8 and YVTe2O8 are calculated to be 2.7 and 2.2 eV, respectively, from the UV-vis diffuse reflectance spectra. Powder second harmonic generation (SHG) measurements using 1064 nm radiation reveals that NCS YVSe2O8 has a similar SHG efficiency to that of NH4H2PO4 (ADP). Detailed explanations of the structure-property relationships, effect of lone pair cation size on the macroscopic centricities, and full characterizations including infrared spectroscopy, thermal analyses, and elemental analyses are also presented.