In this paper, we report a detailed investigation of the crystal structure, magnetic, magnetocaloric, magneto-transport and electrical polarization properties of a new multiferroic material in the polycrystalline and nanocrystalline form of the Dy2MnCoO6 double perovskite. Both compounds crystallized in the monoclinic structure with P21/n space group. The magnetic properties of both systems are mainly dominant ferromagnetic (FM) and weak antiferromagnetic (AFM). The FM/AFM coupling is related by the competing and combining functions of the radius and the magnetic moments of rare earth ions (i.e. 3d–4f exchange interactions). The reduction of the saturation magnetization in the isothermal magnetization curves can be explained by the existence of anti-phase boundaries and local anti-site defects in the system. Moreover, these materials hold reasonable values of magnetocaloric parameters and the absence of hysteresis makes the system a potential candidate for magnetic refrigeration. These compounds revealed two magnetic phase transitions, according to the appearance of two peaks in the temperature dependence of magnetic entropy change curves. The temperature dependent resistivity data for both the systems display semiconductor nature near room temperature and insulating like behavior at low temperature regime. The variable-range hopping conduction mechanism is used to best understand their transport mechanism. In addition, the electrical polarization loop at low temperature confirms the presence of ferroelectricity for both the studied systems. The decreases polarization under an external magnetic field evidence the weak magnetoelectric coupling. The coexistence of FM ordering with insulating behavior and ferroelectricity at low temperature promises new opportunities and improvements in next generation applications for information storage, spintronic, and sensors.