A deep learning algorithm for Gaussian noise removal from both grayscale and color images is developed. As opposed to most existing discriminative methods that train a specific model for each noise level, the proposed method can handle a wide range of noise levels using only two trained models, one for low noise levels and the other for high noise levels. In the proposed algorithm, the training process consists of three successive steps. In the first step, a classifier is trained to classify the noisy and clean images. In the second step, a denoiser network aims to remove the noise in the image features that are extracted by the trained classifier. Finally, a decoder is utilized to map back the denoised images features into images pixels. To evaluate the performance of the model, the Berkeley segmentation dataset of 68 images (BSDS68) and 12 widely used images are used, and the denoising performance for additive white Gaussian noise is compared with several state-of-the-art methods in terms of peak signal-to-noise ratio (PSNR) and visual quality. For grayscale image denoising of BSDS68, our method gives the highest PSNR on all noise levels (significant mean improvement of 0.99). For color image denoising of BSDS68, except for one low noise level, the proposed method gives the highest PSNR on all other noise levels (mean improvement of 0.3).