The system of lead free piezoelectric ceramics, (1-x)(0.94Bi0.5Na0.5TiO3-0.06BaTiO3)-xBaSnO3 [abbreviated as BNT-BT-xBSn] with the compositions, x = 0.00, 0.02, 0.04, 0.06, 0.08 and 0.10 was synthesized via the conventional solid state reaction method. All the products from X-ray diffraction patterns showed diffraction peaks as a phase perovskite structure, with no secondary phases. Due to the composition-dependence of the ferroelectric, bipolar and unipolar strain properties were investigated in order to achieve a good new lead free piezoelectric ceramics system. It was noticeable that a large strain of around 0.4%, with a normalized strain value (d33*) of 669 pm/V at the x = 0.02composition, by applying an electric field of 60 kV/cm at room temperature. The results of this study showed that a new BNT-BT-xBSn ceramics system is a very promising candidate for creating a significantly large strain response, which is sufficiently effective for actuator material applications.