Element bismuth (Bi) will experience complex phase transitions under high temperature and high pressure, which means significant changes in physical properties, such as density, energy, etc. Multiphase equations of states (EOSs) of both solid and liquid phases for Bi are presented. The EOSs are based on the three-term expression for Helmholtz free energy, where the ion vibration free energy is evaluated from the mean field potential model we recently proposed. The calculated results show that our multiphase EOSs can well reproduce the experimental data, including phase diagram, isotherms of solid phases, density measurements of liquid phase and shock-wave compression data, which proves the rationality of the parameter values and the universal nature of this model.