This paper proposes a single-channel speech enhancement method to reduce the noise and enhance speech at low signal-to-noise ratio (SNR) levels and non-stationary noise conditions. Specifically, we focus on modeling the noise using a Gaussian mixture model (GMM) based on a multi-stage process with a parametric Wiener filter. The proposed noise model estimates a more accurate noise power spectral density (PSD), and allows for better generalization under various noise conditions compared to traditional Wiener filtering methods. Simulations show that the proposed approach can achieve better performance in terms of speech quality (PESQ) and intelligibility (STOI) at low SNR levels.