Studies on lead-free piezoelectrics have been attractive as means of meeting environmental requirements. We synthesized lead-free piezoelectric $(Bi_{1/2}Na_{1/2})TiO_3-Ba(Cu_{1/3}Nb_{2/3})O_3$ (BNT-BCN) ceramics, and their dielectric, piezoelectric, and strain behavior were characterized. As BCN with a tetragonal phase was incorporated into the rhombohedral BNT lattice, the lattice constant increased. A small amount of BCN increased the density and dielectric constant forming the complete solid solution with BNT. However, BCN above 10 mol% was precipitated into a separate phase, and which was detected with XRD. In addition, EDX measurement revealed that Cu in BCN was not distributed homogeneously but was accumulated in a certain area. A lower density with a large amount of BCN was attributed to the nonsinterable property of BCN with large tetragonaliy. The dielectric constant vs the temperature change and the strain vs the electric field indicated that the ferroelectric property of BNT was diminished and paraelectric behavior was enhanced with the BCN addition. BNT-7.5BCN showed a 0.11% unimorph strain with a 9.0 kV/mm electric field with little hysteresis.