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Noise suppression of diffusion noise by microphone arrays is discussed in this paper. In our previous work, we proposed a method for jointly estimating signal and noise correlation matrices from observations with diffusion noise by using so-called crystal shape microphone arrays; and discussed the performance of the Wiener filter based on those correlation matrices. In this paper, we propose a novel method for noise suppression of diffusion noise based on the newly adopted spectral subtraction scheme with the estimated correlation matrices by our previous work. We also verify the efficacy of the proposed method by some computer simulations and show that the proposed method outperforms our previous method by the Wiener filter.