Digital holography is a very efficient technique for 3D imaging and the characterization of changes at the surfaces of objects. However, during the process of holographic interferometry, the reconstructed phase images suffer from speckle noise. In this paper, de-noising is addressed with phase images corrupted with speckle noise. To do so, DnCNN residual networks with different depths were built and trained with various holographic noisy phase data. The possibility of using a network pre-trained on natural images with Gaussian noise is also investigated. All models are evaluated in terms of phase error with HOLODEEP benchmark data and with three unseen images corresponding to different experimental conditions. The best results are obtained using a network with only four convolutional blocks and trained with a wide range of noisy phase patterns.