The structure, electric field-induced strain (EFIS), polarization and piezoelectric response of lead-free Sr₃FeNb₂O₉-modified (Bi_1/2Na_1/2)_0.935Ba_0.065TiO₃ (BNBT–xSFN, with x = 0–0.012) ceramics were investigated. XRD patterns show that all compositions have a pure perovskite structure and SFN effectively diffused into the BNBT lattice during sintering to form a solid solution. A large EFIS of 0.35% was obtained at the critical composition of x = 0.009 which corresponds to a normalized strain (S_max/E_max) of 583 pm V⁻¹. A maximum value of piezoelectric constant (254 pC N⁻¹) was obtained for x = 0.006. These results show our research can benefit the developments of Bi_1/2Na_1/2TiO₃ ceramics and widen their range of applications.