The (1-x)(0.8Bi(1/2)Na(1/2)TiO(3)-0.2Bi(1/2)K(1/2)TiO(3))-xBiMg(2/3)Nb(1/3)O(3) (100xBMN) ternary solid solutions were designed and prepared using a conventional solid-state reaction. Temperature and compositional dependent ferroelectric, piezoelectric, dielectric features, and structural evolution were systematically studied. At the critical composition of 2BMN, a large bipolar strain of 0.43% was achieved at 55kV/cm, and the normalized strain reaches to 862pm/V at a low driving electric field of 40kV/cm. It was found that the substitution of BiMg2/3Nb1/3O3 induces a transformation from ferroelectric to relaxor phase by disrupting the long range ferroelectric order. Therefore, as the external electric field was applied, a relaxor-ferroelectric phase transition will be induced. This is contributed to the giant strain. The results above suggest that such a ternary composition is a promising candidate for application to actuator.