Abstract: Fast muhipole method is used for lossy half-space environment arbitrary three-dimensional PEC radar scattering properties. For basis functions and test functions within the near-field. The nearby terms in the FMM framework are evaluated by using the rigorous half-space dyadic Green＇s function, computed via the method of complex images. Non-near （far） FMM interactions are modeled as in the free-space FMM, with the dyadic Green＇s function approximated via real ima- ges and equivalent reflection coefficients, these approximations have proven to be highly accurate, for a large trihedral fidu- cial target and rectangular box, above a lossy half space. Further we use a muhiresolution （MR） preconditioner to precondition the modified FMM, the result shows the MR preconditioner can speed up the convergence rate of the FMM quite well. And this method is extended to the fast multipole method, makes more practical significance.