$(Bi_{1/2}Na_{1/2})TiO_3$-based ceramics have been intensively studied as lead-free piezoelectric ceramics. In this study, the piezoelectric properties and phase transition behaviors of BNT based solid solution $(Bi_{0.5}Na_{0.5})_{1-x}Ca_xTiO_3$ ($X=0.01{sim}0.25$) were investigated. The morphotropic phase boundary(MPB) zone which BNT is transformed from rhombohedral to cubic structure was appeared by adding $CaTiO_3$ with 0.12 mol by the measurement of permittivity and X-ray diffraction. The behavior which ferroelectric BNT with adding $CaTiO_3$ was changed to antiferroelectric and paraelectric state was confirmed by the measurement ofhysterisis loop and depolarization temperature as a function of temperature. As $CaTiO_3$ concentration was increased, the phase transition temperature was decreased. The piezoelectric properties were highest at 0.01 mol of $CaTiO_3$ concentration. The electromechanical coupling factor($K_t$) and mechanical quality factor($Q_m$) were 42% and 254, respectively.