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A novel 3D shape optimization algorithm is presented for electromagnetic devices carrying eddy current. The algorithm integrates the 3D finite element performance analysis and the steepest descent method with design sensitivity and mesh relocation method. For the design sensitivity formula, the adjoint variable vector is defined in complex form based on the 3D finite element method for eddy current problems. A new 3D mesh relocation method is also proposed using the deformation theory of the elastic body under stress to renew the mesh as the shape changes. The design sensitivity for the surface nodal points is also systematically converted into that for the design variables for the parameterized optimization application. The proposed algorithm is applied to the optimum design of the tank shield model of transformer and the effectiveness is proved.