Polarization measurements of X-rays and soft gamma rays can reveal the geometry of the emission region, magnetic field structures, radiation mechanisms, and the environment along the propagation path, serving as a probe for astrophysical research. The Wide Band X-ray Polarization and imaging Telescope (WXPT) can perform polarization measurements over 3~500 keV, filling the gap in hard X-ray and soft gamma-ray polarimetry. The wide-field soft gamma-ray polarimeter is an important payload on this telescope, covering 50~500 keV, and is composed of a plastic scintillator and CsI. Using Geant4, we carried out physics simulations of the wide-field soft gamma-ray polarimeter. The results show a detection efficiency greater than 15% and a minimum detectable polarization (MDP) of 8%.