The (1−x) (Bi0.5Na0.5)TiO3−xBa(Al0.5Ta0.5)O3((1−x)BNT-xBAT) lead-free piezoceramics was fabricated using a conventional solid-state reaction method. The temperature and composition-dependent strain behavior, dielectric, ferroelectric (FE), piezoelectric, and pyroelectric properties have been systematically investigated to develop lead-free piezoelectric materials with large strain response for actuator application. As the BAT content increased, the FE order is disrupted resulting in a degradation of the remanent polarization, coercive field, and the depolarization temperature (Td). A large strain of 0.36% with normalized strain d33* = 448pm/V was obtained for the optimum composition x = 0.045 at room temperature. The bipolar and unipolar strains for the compositions x = 0.035 and x = 0.04 reach almost identical maximum values when the temperature is in the vicinity of their respective depolarization temperature (Td). The Raman-spectra analysis, macroscopic properties, thermal depolarization results, and temperature-dependent relationships of both polarization and strain demonstrated that the origin of the large strain response for this investigated system is attributed to a field-induced relaxor to FE phase transformation.