In this work, we propose a parameter-free and efficient method to tackle the structure-texture image decomposition problem. In particular, we present a neural network LPR-NET based on the unrolling of the Low Patch Rank model. On the one hand, this allows us to automatically learn parameters from data, and on the other hand to be computationally faster while obtaining qualitatively similar results compared to traditional iterative model-based methods. Moreover, despite being trained on synthetic images, numerical experiments show the ability of our network to generalize well when applied to natural images.