Abstract: In order to improve the Ambiguity-to-Signal Ratio (ASR) of spaceborne SAR, an adaptive Genetic Algorithm (GA) is proposed in this paper. By using the algorithm, ASR and antenna pattern are optimized simultaneously. Firstly，the ambiguity areas are determined, then the beamwidth and the side lobe level (including the side lobe level in the ambiguity areas of spaceborne SAR) of the antenna pattern are regarded as the objective function to synthesis the antenna pattern by using the adaptive GA. In order to avoid premature convergence, the crossover rate, the mutation rate and the mutation range are simultaneously adaptive during the optimization process. Compared to non-adaptive GA, the adaptive GA requires less iteration to converge and converges faster. The simulation results show that the ambiguity is depressed well via this method, which is quite useful to spaceborne SAR system designing.