In the context of practical engineering, establishing an effective multi-physical-field coupling simulation model for annular linear induction electromagnetic pumps is crucial for structural optimization and performance improvement of electromagnetic pumps. This paper relies on the research and development of a prototype annular linear induction electromagnetic pump for a sodium-cooled fast reactor to construct a three-dimensional finite element simulation (FEM) model of the electromagnetic pump’s electrical, thermal, and fluid multi-physical-field coupling in the sodium-cooled fast reactor environment. The model couples Maxwell’s equations with the Navier-Stokes equations. For the sodium fluid region, a magnetohydrodynamic (MHD) coupling equation is established, while a two-phase heat transfer model for fluid and solid is introduced to describe the thermal flow field. Maxwell’s equations are used to characterize the electromagnetic field in the extra-flow region and solve for the magnetic vector potential. The validity of the model is verified through experimental data under no-load conditions. Combined with the simulation results of physical quantities such as magnetic flux density, Lorentz force, velocity, pressure, and temperature inside the EM pump, the working principle and technical details of the EM pump are analyzed, and the performance and efficiency of the prototype EM pump are predicted. The relevant work provides certain reference value for engineering design and application in the field of EM pumps.