For multichannel speech enhancement, this letter derives a robust maximum likelihood distortionless response beamformer by modeling speech sparse priors with a complex generalized Gaussian distribution, where we refer to as the CGGD-MLDR beamformer. The proposed beamformer can be regarded as a generalization of the minimum power distortionless response beamformer and its improved variations. For narrowband applications, we also reveal that the proposed beamformer reduces to the minimum dispersion distortionless response beamformer, which has been derived with the ${{\ell}_{p}}$-norm minimization. The mechanisms of the proposed beamformer in improving the robustness are clearly pointed out and experimental results show its better performance in PESQ improvement.