Abstract: The generalized weighted prediction error (GWPE) algorithm is an effective multi-channel speech dereverberation algorithm, but its performance deteriorates when the microphone spacing is small. This paper analyzes the limitations of the GWPE algorithm in small microphone arrays, i. e., it does not fully consider the spatial correlation between microphone signals. Then the generalized weighted prediction error using full-space correlation matrix (GWPE-FCM) algorithm is introduced, which takes into account the spatial correlation between different input channels and slightly increases computational complexity in comparison with the GWPE algorithm. The simulation results show that compared to the GWPE algorithm, the GWPE-FCM algorithm performs better in overall dereverberation, especially when the microphone distance is close. PESQ increased by about 0.2 and STOI increased by about 0.1.