In order to accurately estimate the target azimuth and recovery noise-plus-interference covariance matrix in beamforming, a robust beamforming method based on sparse representation is proposed under the nested array structure. In the proposed method, firstly, the sampled covariance matrix of the nested array is calculated, and a large-aperture virtual uniform line array is obtained by difference co-array processing. Then, the accurate information of the azimuth of the target is estimated based on a sparse representation method. Using the azimuth information, the power value of the interference signal can be calculated by the least squares method. After obtaining the accurate azimuth information and the power value of the interference, the interference plus noise covariance matrix is further reconstructed, and finally the interference suppression is obtained by beamforming method. Experimental simulation shows that the output Signal to Interference plus Noise Ratio(SINR) can approach the optimal output of SINR under different SNR and snapshots, which verifies the effectiveness of the proposed method.