A-site-ordered perovskite Ce1/2Cu3Ti4O12 has been found to crystallize in two different forms, one with random and the other with ordered Ce/vacancy distribution at the A site of the prototype AA(3)'B4O12 structure. The random phase is isostructural with CaCu3Ti4O12, and the ordered phase is a new ordered derivative of the AA(3)'B4O12-type perovskite with two crystallographically distinct Cu sites. Although both phases form a G-type antiferromagnetic arrangement of Cu2+ spins below 24 K, their magnetisms are quite different. A typical antiferromagnetic transition is observed in the random phase, whereas a small ferromagnetic moment appears below 24 K in the ordered phase, which rapidly decreases upon further cooling. A mean-field approximation approach revealed that this unusual behavior in the ordered phase is an L-type ferrimagnetism driven by the nonequivalent magnetizations of the two ferromagnetic Cu2+ spin sublattices in the G-type spin structure. This unusual ferrimagnetism is a direct consequence of the Ce/vacancy ordering.