Abstract: The go-stop assumption applied to the conventional SAR can not be used in the SAR system using step frequency waveforms. For the reason that the time spent on the coherent processing is too long. Accordingly the fast-time Doppler effect induced by the movement of the radar platform can not be neglected as usual. In this paper, a new wavenumber domain based on fast-time Doppler effect compensation method is proposed. This new method is implemented through 2D-FFT and 2D-IFFT.Comparing with the time domain compensation method, the new method has almost the same compensation precision but with less processing time, which is more beneficial to the real-time compensation in the practical step-frequency SAR system.