As the beamforming of Nonuniform Linear Array (NLA) may occur grating lobes phenomenon, a beamforming method is proposed for working on the NLA with consecutive difference coarray. Firstly, this method analyzes the array optimization of the NLA based on consecutive difference coarray. Additionally, it can be concluded that the consecutive difference coarray is corresponding to the consecutive wavepath difference, which is applied to reconstruct the Toeplitz covariance matrix of the NLA. According to the Least Constraint Mean Variance (LCMV) rule, the reconstructed covariance matrix can directly be used for robust adaptive beamforming. Due to the similarity between the reconstructed covariance matrix and the covariance matrix of Uniform Linear Array (ULA) with the same aperture, the phase ambiguity will not happen and the grating lobes phenomenon will not occur. Extensive simulations show the robust effectiveness of the proposed method.