Nonnegative matrix factorization (NMF) is a useful decomposition technique for multivariate data. More recently, NMF technology was used as a noise-estimation stage for a Wiener-filtering-based noise reduction (NR) method to improve the quality of noisy speech. Previous studies showed that this method provides better sound quality performance than conventional NMF-based approaches; however, there is still scope for improving the performance under noisy listening conditions. More specifically, the performance of an NMF noise estimator for calculating the noise level is considered sensitive to diverse noise environments and signal-to-noise ratio conditions. Therefore, we proposed an adaptive algorithm that derives an adaptive factor ($\alpha $ ) to adjust the weight between the estimated speech and noise levels on the basis of the signal-to-noise level for the gain function of the Wiener-filtering-based NR method to further improve the sound quality. Two objective evaluations and listening tests evaluated the benefits of the proposed method, and experimental results show that better output sound quality and competed for speech intelligibility performance can be achieved when compared with conventional unsupervised NR and NMF-based methods.