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This paper presents an efficient real-coefficient fitting both Green’s function and its gradient with Fast Fourier Transform (RFGG-FG-FFT) with cube polynomial inter/extrapolation method (CPIE), which is established for the analysis of scattering from antenna over a wide frequency. To improve the computation efficiency, the CPIE is utilized. In order to reduce memory requirements and accelerate matrix vector multiplication, the RFGG-FG-FFT is adopted. The accuracy, correctness and efficiency of the new method are researched on some examples. Compared with the direct method, the examples show that the new method is superior in broadband without loss of accuracy.