Accurate image segmentation is an essential step in image processing. Gaussian mixture model (GMM) has been widely used for image segmentation due to its low complexity and high accuracy. However, the model assumes that the intensity distributions of images are symmetric, which makes it hard to obtain ideal results for images with asymmetric distributions. In addition, the model does not consider any noise, which makes it difficult to obtain ideal distribution fitting results when the image contains severe noises. Furthermore, the model only considers the distribution information without any spatial information, so it is sensitive to noise when segmenting images. To address these issues, we model noise with a Gaussian distribution and couple it into a skewed normal mixture model to reduce the effect of asymmetric distributions and noise and can obtain more accurate distribution fitting results. To further reduce the effect of noise, we propose a new anisotropic spatial information constraint term that preserves detailed information while reducing the effect of noise. Finally, an improved EM algorithm is proposed to solve the parameters of the model. Experimental results on synthetic and natural images show that our method achieves better segmentation results compared to other models.