The structure of the new polar oxide, Cd₂InVO₆, was determined by powder X-ray diffraction. Cd₂InVO₆ crystallizes in space group P3₁ with the unit cell parameters: a = 12.21896(4), c = 9.25675(4) Å. The Cd²⁺ and In³⁺ ions are statistically disordered in nine independent positions (M1−M9) with a certain level of site preference. M1−M3 form highly asymmetric oxygen-coordination polyhedra, which are similar to those formed by alkali or alkali-earth cations. M4−M9 are in distorted octahedral cavities. It is shown that M1−M3 are likely occupied mostly by Cd²⁺ while M4−M9 are extensively mixed by Cd²⁺ and In³⁺. The structure is best described as a framework of interconnected M4−M9 distorted octahedra with the M1−M3 polyhedra off-framework and the three independent VO₄ tetrahedra filling the channels of the framework structure by corner-sharing with the MO₆ octahedra. The polar framework is composed of M4O₆M9O₆ octahedra in a five-connected net with the topology nomination (3³, 6³, 9⁴). The Bi³⁺-substituted compounds were also investigated with the rationale that the lone pair electrons of Bi³⁺ might enhance ferroelectricity. Single phase Cd_1−xBi_x(Cd_1+xIn_1−x)VO₆ forms limited solid solutions (0.02 ≤ x ≤ 0.14). Ferroelectricity was observed for neither the parent nor the Bi³⁺-substituted compounds, which suggest that the dipole moments are not switchable or too insignificant in magnitude. The powder second-harmonic generation measurements with 1064 nm radiation established that Cd_1−xBi_x(Cd_1+xIn_1−x)VO₆ are type-1 phase-matchable materials for x = 0, 0.14 with 70 and 90 times the efficiency of α-SiO₂, respectively.