Abstract: In this paper,a fast beam optimization algorithm for spaceborne Synthetic Aperture Radar(SAR)is proposed.By using this algorithm, the beam of spaceborne SAR antenna is optimized, and the ambiguity areas are depressed.Firstly, the complex value of the array pattern is obtained by using an inverse Fast Fourier transform(IFFT).Then compared to the desired pattern,all the values of the pattern exceeding the desired pattern are replaced by the values of the desired pattern.Repeat the above operation until the array pattern satisfies the pattern requirements.Compared with the conventional methods, the proposed algorithm needs no complicated operation.Therefore, it provides significant improvements in terms of computational speed and optimization time.Two examples are presented to demonstrate the high efficiency and practicality of the method.