In this letter, a multichannel decision-directed approach to estimate the speech power spectral density (PSD) matrix for multichannel speech enhancement is proposed. There have been attempts to build multichannel speech enhancement filters which depend only on the speech and noise PSD matrices, for which the accurate estimate of the clean speech PSD matrix is crucial for a successful noise reduction. In contrast to the maximum likelihood estimator which has been applied conventionally, the proposed decision-directed method is capable of tracking the time-varying speech characteristics more robustly and improves the noise reduction performance under various noise environments.