A YBCO superconductor prepared by a Melt Powdering Melt Growth (MPMG) method was investigated with respect to the feasibility for an application to a superconducting current lead. A thermal conductivity and a critical current density of the YBCO sample were measured in the temperature range from 50 K to 15 K. The value of the thermal conductivity was about 0.03 W/cmK at 50 K. In the sample with a cross section of 8.65 × 6.85 mm2 and a thickness of 2.25 mm, the maximum quench current at 26 K was 86 A of which the value was one of few tens of the value expected from the critical current density, about 3000 A/cm2. The contact resistance at the current junction was relatively high, about 0.5 mΩ. Obtained results indicate that the MPMG bulk is a hopeful material for a superconducting current lead.