Double perovskites Re2CoMnO6 Dy) have been synthesized by a solid-state reaction method. Magnetic field-induced metamagnetic behavior is observed in the samples below the ferromagnetic Curie temperature (T-c), which are respectively 123 K and 88 K in Sm2CoMnO6 and Dy2CoMnO6. The origin of this effect is attributed to the competition between the nearest-neighbor ferromagnetic super exchange interaction (Co2+-Mn4+) and the next nearest-neighbor antiferromagnetic exchange interaction (Co2+-Co2+, Mn4+-Mn4+). Arrott plots combined with the thermal hysteresis confirm that the transition from ferromagnetic to antiferromagnetic state with negative slope is the first-order magnetic phase transition. Moreover, the positive slope closely to Tc indicates that the transition from paramagnetic to ferromagnetic state is the second-order transition. Magnetocaloric effect associated with Maxwell's relation is studied and the maximal value of |Delta S-M| is 1.4 and 3.5 J kg(-1) K-1 at 6 T near T-C for Sm2CoMnO6 and Dy2CoMnO6. The large value of |Delta S-M| for Dy2CoMnO6 is obtained which is 9.1 J kg(-1) K-1 at 20 K. The relatively smaller magneto entropy change for Sm2CoMnO6 may be attributed to the higher coercive field and the weaker magnetism. (C) 2017 Elsevier B.V. All rights reserved.