In this paper, we propose a noise reduction method based on non-negative matrix factorization (NMF) for noise-robust automatic speech recognition (ASR). Most noise reduction methods applied to ASR front-ends have been developed for suppressing background noise that is assumed to be stationary rather than non-stationary. Instead, the proposed method attenuates non-target noise by a hybrid approach that combines a Wiener filtering and an NMF technique. This is motivated by the fact that Wiener filtering and NMF are suitable for reduction of stationary and non-stationary noise, respectively. It is shown from ASR experiments that an ASR system employing the proposed approach improves the average word error rate by 11.9%, 22.4%, and 5.2%, compared to systems employing the two-stage mel-warped Wiener filter, the minimum mean square error log-spectral amplitude estimator, and NMF with a Wiener post-filter, respectively.