Clutter suppression presents crucial importance for Ground Penetrating Radar (GPR) images since clutter decreases considerably target detection rates. Robust Principal Component Analysis (RPCA) is widely used to remove clutter. However, RPCA requires sequential singular value decomposition (SVD) operations in each iteration, and thus computational cost and run-time increase. Also, the hyperparameter should be set manually. In this paper we propose to use unfolding techniques by converting each iteration to a single layer of the network and train the resulting Convolutional Neural Network (CNN) structure to learn the separation of GPR images into clutter and target components. The proposed method is compared to SVD, traditional RPCA , SVD free RNMF and learning based RAE. The recently introduced public hybrid dataset is used for training. The visual and quantitative results validate a performance which approximates RPCA while outperforming RAE with running times less than in any of the existing methods.