Abstract: In this paper, a divided region variational principle to solve 3-D eddy current problems was given. It adopts the magnetic vector potential A and the electric scalar potential φ in the eddy current regions and the source regions, and the magnetic scalar potential Ω in the non-conducting regions (air gap). Using variation of the functional all governing equations in various regions, the natural boundary conditions and the interface continuity conditions which satify electromagnetic continuity are obtained.