This paper introduces the Spatially Preprocessed Speech Distortion Weighted Multi-channel Wiener Filter (SP-SDW-MWF) for multi-microphone noise reduction and proposes a method to determine the speech distortion weights. The SP-SDW-MWF is known as a robust noise reduction algorithm against the error caused by the mismatch in microphones. The SP-SDW-MWF adopts weights which determine the amount of noise reduction at the expense of introducing speech distortion in the noise-suppressed speech. In this paper, we use the error of power spectral density between the estimated signal and the desired signal as the evaluation measure. Thus the a priori SNR is used to control the speech distortion weights in the frequency domain. In the experimental results, the proposed method yields better result in terms of MFCC distortion compared to the conventional method.