LaRNiMnO6 (R = Pr, Nd, Sm) double perovskite ceramics were designed and synthesized, and their dielectric, magnetic and magnetodielectric characteristics were evaluated together with the structure. The crystal structure was determined as monoclinic in space group P21/n, and the dense ceramics could be obtained by a solid state reaction process. A ferromagnetic transition similar to that in La2NiMnO6 occurred in LaRNiMnO6 ceramics and the TC point decreased with decreasing ionic radius of R. The significant magnetodielectric effect was determined and the maximum magnetodielectric coefficient up to −7.7% was obtained in LaSmNiMnO6. Moreover, a dielectric anomaly around the magnetic TC was detected for the present ceramics which also indicated the magnetodielectric coupling.