The generalized sidelobe cancellation (GSC) is a commonly used adaptive beamforming technology, which can be used in antenna arrays. Due to the error of the direction of arrival of the received signal and the spacing error of the received array elements, the signal received by the array antenna has a mismatch of steering vectors, which leads to that the GSC method cannot accurately aim at the expected signal and suppress the interference signal. In order to improve the robustness of GSC algorithm, a new adaptive beamforming algorithm named SGSC (Sequential Quadratic Programming-Generalized Side Lobe Cancellation) is proposed in this paper. In this method, firstly, the mismatching expected signal steering vector is corrected by the stepwise quadratic programming, so that the auxiliary antenna can effectively block the expected signal. Then, the optimal weight vector is obtained by combining the corrected steering vector with the GSC, so that the expected signal components of the auxiliary antenna and of the main antenna can be avoided from being cancelled due to mismatch errors. Finally, the simulation results based on MATLAB show that the new algorithm can point the desired signal more accurately and suppress the interference signal more obviously in the presence of mismatch error, which shows the effectiveness of the method.