This study shows a new lead-free piezoelectric system (1-x)Na0.5Bi0.5TiO3-xBi(Zn0.5Zr0.5)O-3 [(1-x)NBT-xBZZ, x=0, 0.02, 0.03, 0.035, 0.04 and 0.05]. The structure of Bi(Zn0.5Zr0.5)O-3 was calculated with first-principles method. A morphotropic phase boundary (MPB) near x=0.03 between rhombohedral and pseudo-cubic phases was found, and its improvement in electrical properties was demonstrated. In the MPB composition, the maximum polarization, remnant polarization, coercive field and piezoelectric coefficient are 46.4 mu C/cm(2), 39.2 mu C/cm(2), 4.8 kV/mm and 95 pC/N, respectively. The results not only show a new lead-free piezoelectric system but also suggest a new route to designing lead-free piezoelectric materials. (C) 2015 Elsevier Ltd and Techna Group S.r.l. All rights reserved.