Relaxor ferroelectrics (0.94-x)(Bi0.5Na0.5)TiO3-0.06BaTiO(3-x)(Sr0.7Bi0.20.1)TiO3 (BNT-BT-xSBT) (0x0.5), were prepared by a solid-state reaction process, and their structures were characterized by the transmission electron microscopy and Raman spectroscopy. The BNT-BT-0.3SBT has a very high electrostrictive strain S=0.152% with hysteresis-free behavior, much more than the reported S in other ferroelectrics. S-P-2 profiles perfectly follow the quadratic relation, which indicates a purely electrostrictive effect with a high electrostrictive coefficient (Q(11)) of 0.0297m(4)/C-2. Even, its Q(11) keeps at a high level in the temperature range from ambient temperature to 180 degrees C. The field-induced large electrostrictive strain of BNT-BT-0.3SBT was attributed to the existence of ferroelectric nanodomains.