The 0.45Bi(Mg0.5Ti0.5)O3-(0.55-x)PbTiO3-x(Bi0.5Na0.5)TiO3 (BMT-PT-xBNT) ternary solid solution ceramics were prepared via a conventional solid-state reaction method; the evolution of dielectric relaxor behavior and the electrostrain features were investigated. The XRD and dielectric measurements showed that all studied compositions own a single pseudocubic perovskite structure and undergo a diffuse-to-relaxor phase transition owing to the evolution of the domain from a frozen state to a dynamic state. The formation of the above dielectric relaxor behavior was further confirmed by a couple of measurements such as polarization loops, polarization current density curves, as well as bipolar strain loops. A large strain value of similar to 0.41% at a driving field of 7kV/mm (normalized strain d33* of similar to 590pm/V) was obtained at room temperature for the composition with x=0.32, which is located near the boundary between ergodic and nonergodic relaxor. Moreover, this electric field-induced large strain was found to own a frequency-insensitive characteristic.