Magnetoelectric multiferroicity is not expected to occur in a cubic perovskite system because of the high structural symmetry. By versatile measurements in magnetization, dielectric constant, electric polarization, neutron and x-ray diffraction, Raman scattering, as well as theoretical calculations, we reveal that the A-site ordered perovskite LaMn(3)Cr(4)O(12) with cubic symmetry is a novel spin-driven multiferroic system with strong magnetoelectric coupling effects. When a magnetic field is applied in parallel (perpendicular) to an electric field, the ferroelectric polarization can be enhanced (suppressed) significantly. The unique multiferroic phenomenon observed in this cubic perovskite cannot be understood by conventional spin-driven microscopic mechanisms. Instead, a nontrivial effect involving the interactions between two magnetic sublattices is likely to play a crucial role.