Lead free positive temperature coefficient of resistivity (PTCR) ceramics based on $BaTiO_3-(Bi_{0.5}Na_{0.5})TiO_3$ solid solution were prepared by a conventional solid state reaction method. The phase structure was showed single phase with perovskite structure regardless calcinations temperature and $Ba_{1-x}(Bi_{0.5}Na_{0.5})_xTiO_3$ structure was transformed from tetragonal to orthorhombic phase at $x{geq}0.15$ mole. The XRD peaks with $45^{circ}{sim}46^{circ}$ shifted in right the influence of crystal structure change and the intensity of peak was decreased with additive $(Bi_{0.5}Na_{0.5})TiO_3$. The curie temperature risen with additive $(Bi_{0.5}Na_{0.5})TiO_3$ but disappeared for $(Bi_{0.5}Na_{0.5})TiO_3$ addition more than 0.15 mole in TMA. In relative permittivity, the curie temperature by the transform of ferroelectric phase risen with additive $(Bi_{0.5}Na_{0.5})TiO_3$ but decreased in relative permittivity. Also, the peak of new curie temperature showed the sample containing $0.025{sim}0.045$ mole of $(Bi_{0.5}Na_{0.5})TiO_3$ near $70^{circ}C$ caused by phase transform from ferroelectric to ferroelectric and the peak of new curie temperature disappeared at 0.045 mole of $(Bi_{0.5}Na_{0.5})TiO_3$. In our study, it was found that the PTCR in $BaTiO_3-(Bi_{0.5}Na_{0.5})TiO_3$ system was possible for $0{sim}0.025$ mole of $(Bi_{0.5}Na_{0.5})TiO_3$ and the maximum curie temperature by phase transition showed about at $145^{circ}C$.