The phase structure, dielectric and piezoelectric properties of a new lead-free piezoelectric system (1 - x) Bi0.5Na0.5TiO3-xBi(Zn0.5Hf0.5)O-3 [(1 - x) BNT-xBZH, x 0, 0.01, 0.02, 0.03, and 0.04] were investigated. The structure of Bi(Zn0.5Hf0.5)O-3 was calculated using first-principles method and (1 - x) BNT-xBZH ceramics were fabricated by conventional solid-state process. At room temperature, a morphotropic phase boundary (MPB) from rhombohedral to pseudocubic is identified near x 0.02 by the analysis of X-ray diffraction patterns. The ceramics with MPB near room temperature exhibit excellent electrical properties: the Curie temperature, maximum polarization, remnant polarization, and coercive field are 340 degrees C, 56.3 mu C/cm(2), 43.5 mu C/cm(2), and 5.4 kV/mm, respectively, while the maximum positive bipolar strain and piezoelectric coefficient are 0.09% and 92 pC/N, respectively. In addition, a linear relationship between the MPB phase boundary composition and the calculated tetragonality of non-BNT end-member was demonstrated. Thus, this study not only shows a new BNT-based lead-free piezoelectric system but also suggest a new way to predict the composition at MPB a priori when designing new lead-free piezoelectric system. (C) 2014 AIP Publishing LLC.