Abstract: This paper proposes a jointly denoising and dereverberation beamformer based on a complex super-Gaussian distribution. By modelling speech using a complex super-Gaussian distribution， we first derive the optimal denoising and dereverberation beamformer with a maximum likelihood criterion. The paper further proves that the proposed beamformer can be regarded as a generalized framework of many existing jointly denoising and dereverberation methods and also demonstrates that the proposed beamformer outperforms the weighted prediction error algorithm cascaded minimum power distortionless beamformer theoretically. Simulation results and experimental results show that the proposed beamformer does outperform many state-of-the-art joint denoising and dereverberation algorithms in terms of several objective measurements.