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Efficient generation of jamming signal is an important but intractable issue in active deception jamming against synthetic aperture radar. Considerations must be given to both the computational complexity and the focus depth of the false scatterers of a deception template. However, existing methods cannot meet both demands mentioned above when generating jamming signal of an extended false scene or scattered false targets. In this study, a frequency-domain three-stage algorithm (FDTSA) is proposed. In theory, the jammer system is deliberately reformatted in the two-dimensional frequency domain. Accordingly, the implementation of the FDTSA can be effectively accelerated by fast Fourier transform and by separating the modulation process of a repeat jammer into three stages: the offline stage, the initialisation stage and the real-time modulation stage. Theoretical analyses and simulation results indicate that the FDTSA can get rid of severe focus deterioration of the false scatterers and reasonable computational load is required.