The perovskite ferroelectric Pb(Zr_xTi_<1-x>)O_3 (PZT) at morphotropic phase boundary (MPB) consist of multiple crystal systems and it shows complicated hysteresis behavior and high piezoelectric responses depending on domain switching and structural phase transition. In the present work, a multiscale nonlinear finite element method based on crystallographic homogenization theory was developed to evaluate nonlinear behaviors at MPB. We employed the incremental constitutive law taking into consideration with material property changes caused by domain switching and structural phase transition and the judgment formulation based on electromechanical energy. Some computational results of typical ferroelectric behaviors were presented for PZT.