Mammography is using low-energy X-rays to screen the human breast and is utilized by radiologists to detect breast cancer. Typically radiologists require a mammogram with impeccable image quality for an accurate diagnosis. In this study, we propose a deep learning method based on Convolutional Neural Networks (CNNs) for mammogram denoising to improve the image quality. We first enhance the noise level and employ Anscombe Transformation (AT) to transform Poisson noise to white Gaussian noise. With this data augmentation, a deep residual network is trained to learn the noise map of the noisy images. We show, that the proposed method can remove not only simulated but also real noise. Furthermore, we also compare our results with state-of-the-art denoising methods, such as BM3D and DNCNN. In an early investigation, we achieved qualitatively better mammogram denoising results.