This paper presents a deep-learning-based algorithm dedicated to the processing of the speckle noise in phase measurements in digital holographic interferometry. In order to train the network to de-noise phase fringe patterns, a database is constituted with a set of noise-free and noisy phase data corresponding to realistic decorrelation phase noise conditions. An iterative scheme coupled with an input noise level estimator allows improving the deep learning based approach especially for strong noise. Performance of the trained network is estimated and shows that this approach is close to the state-of-the-art of speckle de-noising in digital holographic phase measurements.