The multi-channel linear prediction （MCLP） is one of the most popular speech dereverberation methods. The band-to-band spectral subtraction model has been adopted by most existing studies to obtain the desired speech signal in each frequency band， but it neglects the interaction between different frequencies. This paper proposes a MCLP-based speech dereverberation method using the cross-band spectral subtraction model instead of the widely adopted band-to-band spectral subtraction model. The proposed model employs cross-band filters to account for the interactions between different frequencies. We model the desired signal using the complex generalized Gaussian （CGG） distribution. Compared with the Gaussian distribution， the CGG distribution can capture the sparse nature of speech signals using a suitable shape parameter. Within the maximum likelihood estimation framework， the speech dereverberation problem is formulated as an optimization problem involving the band-to-band and cross-band filters. An optimization algorithm with guaranteed convergence is derived based on the majorization-minimization method. A series of speech dereverberation experiments under various reverberation times， different channel numbers and different source-to-microphone distances demonstrate that the proposed method significantly outperforms traditional methods in terms of dereverberation performance.