The magnetic, dielectric, and magnetodielectric properties of La2CoMnO6 ceramics were evaluated together with the polarization-electric field hysteresis loops. The phase segregation consisting of ordered and disordered regions was determined in the present ceramics. The ordering of Co2+ and Mn4+ gave rise to ferromagnetic transition temperature as high as 210 K, while the disordering of Co3+ and Mn3+ resulted in low ferromagnetic transition temperature of 80 and 150 K. The relaxor-like behavior combined with a giant dielectric constant (similar to 105) was determined in La2CoMnO6 ceramics, which was attributed to the charge ordering of Co2+ and Mn4+. Owing to the mutual origin of magnetism and dielectric relaxation, La2CoMnO6 ceramics showed considerable magnetodielectric effects (similar to 0.8% at 10 kOe) at room temperature.