In this paper, a strong coupling between magnetic and electric phenomena is provided allowing to have an accurate and high-speed coupled model. A coupled circuit and magnetic model for an E-core transverse flux permanent magnet linear motor (TFPMLM) is proposed, which has an advantage linked to reducing time computing more than ten times when compared to 3-D finite-element model (FEM). Firstly, a multi-plane flexible-mesh nonlinear equivalent magnetic network (EMN) model is proposed to improve the computation efficiency as well as the high precision of the magnetic model. And a new method to define the converged iterative process is presented to further decrease the computing time. Secondly, the magnetic circuit and electric circuit are normalized into a solution matrix by introducing controlled sources and discretization methods which forms the coupled model. Then, the magnetic flux in the magnetic circuits and the current in the electric circuits are obtained simultaneously for each time step. The characteristics such as the air-gap flux density distribution, output thrust force waveforms and the phase currents are analyzed by the proposed coupled model. The modeling approach is approved by comparison with the 3-D FEM model. Finally, the proposed model is validated through the experimental setup with the machine prototype. INDEX TERMS Coupled model, electric circuit, equivalent magnetic network (EMN), linear motor, transverse flux.