Nd-Fe-B sintered magnets are one of the strongest permanent magnets and are used for traction motors of electric vehicles. The magnetic properties of the Nd-Fe-B magnets, such as coercivity, strongly depend on their microstructures. The microstructure is formed through several manufacturing processes including liquid-phase sintering. Therefore, to realize high-performance magnets, we have to predict and control the microstructural evolution during liquid-phase sintering. Numerical simulation using the phase-field (PF) method is an effective approach to predict the microstructural evolution during sintering process. To date, various PF models of sintering have been proposed. However, no PF model can simultaneously analyze macroscopic densification occurring in sintering and solute diffusion in multiphase and multicomponent systems. In this work, we developed a new multi-phase-field (MPF) model of liquid-phase sintering to predict the microstructural evolution of the Nd-Fe-B sintered magnet. Our MPF model can simultaneously analyze multiple important phenomena for predicting microstructural evolution during liquid-phase sintering: macroscopic densification of sintered compact, grain growth, phase transformation, and multicomponent solute diffusion based on the thermodynamics database provided by the calculation of phase diagram.