Abstract Flow instability is the intricate phenomenon in the annular linear induction pump (ALIP) when the pump runs at off-design working condition. A three-dimensional (3D) numerical model is built to simulate the flow in the pump channel. The pump heads at different flow rates are accurately predicted by comparing with experiment. The simulation results show the fluid velocity is circumferentially nonuniform in the pump channel even at the nominal flow rate. The flow in the middle sector continuously decelerates to nearly zero with the reducing flow rate. Reversed flow occurs in the azimuthal plane, followed by vortex flow. The reason for the heterogeneous velocity field is attributed to the mismatch between nonuniform Lorentz force and relatively even pressure gradient. It is seen that the flow in the region of small Lorentz force has to sacrifice its velocity to match with the pressure gradient. An analytic expression of the axial Lorentz force is then developed and it is clearly demonstrated the Lorentz force could be influenced by the profiles of velocity and radial magnetic flux density. The coupling between velocity and magnetic field is studied by analyzing the magnitudes of different terms in the dimensionless magnetic induction equation. It is found the dissipation term is determined by not only the magnetic Reynolds number but also the square of wave number of the disturbance in each direction. The smaller disturbing wave number weakens the dissipating effect, resulting in the larger nonuniform magnetic field and axial Lorentz force.