Under the criterion of maximum output signal-to-noise ratio (SNR), the problem of difficult control of complex-valued coefficients in Generalized eigenvalue beamforming is encountered, and severe distortion of the output signal can be caused in complex acoustic environments. To address the issue of complex-valued coefficient estimation, a complex-valued coefficient estimation method based on minimum mean square error (MMSE) is proposed in this paper. By introducing a speech distortion weight factor (SDW), the weight relationship between noise reduction and speech distortion is adjusted, thereby proposing a method for Generalized eigenvalue robust beamforming based on SDW-MMSE. The power spectra of the target and noise signals are estimated using maximum likelihood method, and the main generalized eigenvectors are then determined. Furthermore, the complex-valued coefficients are estimated based on SDW-MMSE, and the complex coefficients are combined with the principal generalized eigenvector to obtain the Generalized eigenvalue robust beamforming filter vector based on SDW-MMSE. Through simulation experiments, it is demonstrated that the proposed beamforming method effectively eliminates coherent and incoherent noise, and exhibits robust performance with high output SNR and low speech distortion.