A crossover from the A-site-ordered double-perovskite structure with Im (3) over bar cubic symmetry to the simple-perovskite structure with Pnma orthorhombic symmetry is found in LnMn(3)V(4)O(12) (Ln = La, Nd, Gd, Y, Lu) synthesized under high-pressure conditions. Relatively large Ln(3+) ions (La3+, Nd3+, and Gd3+) induce the a(+)a(+)a(+) in-phase cooperative tilting of the VO6 octahedra, resulting in the A-site-ordered double-perovskite structure with chemical composition Ln(3+)Mn(3)(2+)V(4)(3.75+)O(12). Compounds with small Ln(3+) ions like Y3+ and Lu3+, on the other hand, crystallize with the Pnma simple-perovskite structure with chemical composition (Ln(1/4)(3+)Mn(3/4)(2+))V3.75+O3, where the Ln(3+) and Mn2+ ions are disordered at the A site. The random distribution of the small A-site cation induces the a(-)b(+)a(-) tilting distortion of the VO6 octahedra. The observed phase crossover is well explained by the structural stability calculation based on the bond-valence-sum model, and the most stable crystal structure gives the smallest unit-cell volume. This A-site-cation size-dependent phase transition between the A-site-ordered double-perovskite and A-site-disordered simple-perovskite structures in LnMn(3)V(4)O(12) is thus a result of the structural stability due to the cooperative tilting of the VO6 octahedra. The Mn2+ ions at the A'(A) site contribute local magnetic moments, whereas the V3.75+ ions at the B site play a role in metallic conduction. The observed magnetic behaviors are consistent with the order disorder distribution of the Mn2+ ions at the A site, antiferromagnetism in the A-site-ordered double perovskites, and magnetic spin glass in the A-site-disordered simple perovskites.