Improvised explosive devices pose a significant threat to defence forces and humanitarian demining personnel. They are weapons of modern times, made from non-conventional military materials, rendering them difficult to identify when buried in the ground. Numerous studies focus on detecting these explosive threats and reducing the false alarm rate. However, there are few attempts to identify the detected explosive devices to take proper countermeasures. This paper presents a multi-level projective dictionary learning method to classify ground penetrating radar signals from improvised explosive devices. The proposed dictionary learning method solves three different tasks simultaneously: suppressing background clutter, learning a set of discriminative features for classification, and training a classifier. The suppression of ground clutter is formulated as a low-rank optimization problem with sparse constraints, where a low-rank subspace is learnt from background clutter signals. Dictionary learning is used to transform the target signals into discriminative feature vectors, which are in turn used by the classifier to predict the target class. Experiments were conducted on real radar data. The results showed that the proposed method is more effective than the existing dictionary models and machine learning methods.