The LuFeCuO4 ceramics with a rhombohedral crystal structure in space group R3 similar to m were prepared by a solid-state reaction process, and both the dielectric and magnetic characteristics were investigated. An obvious dielectric relaxation with activation energy of 0.37 eV was observed, which could be well fitted by the modified Debye equation and Arrhenius law. A PE hysteresis loop was observed in the present ceramics at 150 K, with a remnant polarization of 5.78 x 10-2 mu C/cm2 and a coercive field of 10.76 kV/cm. The LuFeCuO4 was antiferromagnetic with TN of 57 K, and a slim hysteresis loop observed at 5 K demonstrated the weak ferromagnetic behavior below Neel temperature. The room-temperature magnetodielectric response in LuFeCuO4 suggested the existence of magneticdielectric coupling.