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We present fundamentals and procedures of a composite grid method (CGM) for determining eddy currents in moving conductors. Based on the finite-element method (FEM), CGM uses two separate mesh grids - one coarse and one fine - to calculate in the global region and local region separately. The results of the coarse mesh are interpolated onto the boundary of the fine mesh as its Dirichlet's condition. Then two equations are solved in the fine mesh region in order to obtain the reaction force on the boundary, which is reacted on the coarse mesh to modify its right-hand-side load vector. And the equations in the coarse mesh are re-solved. The iteration continues until the results converge. The advantage of CGM is that it allows two overlapped grids differing greatly in size to be meshed independently. Also, the program is easy to modularize and thus has great flexibility and adaptability. Above all, it ensures good numerical accuracy in each grid set. As an example indicates, CGM is effective in handling 2-D moving conductor eddy-current problems that are tedious to solve by conventional methods such as re-meshing or using a Lagrange multiplier.