Incremental learning attempts to develop a classifier which learns continuously from a stream of data segregated into different classes. Deep learning approaches suffer from catastrophic forgetting when learning classes incrementally, while most incremental learning approaches require a large amount of training data per class. We examine the problem of incremental learning using only a few training examples, referred to as Few-Shot Incremental Learning (FSIL). To solve this problem, we propose a novel approach inspired by the concept learning model of the hippocampus and the neocortex that represents each image class as centroids and does not suffer from catastrophic forgetting. We evaluate our approach on three class-incremental learning benchmarks: Caltech-101, CUBS-200-2011 and CIFAR- 100 for incremental and few-shot incremental learning and show that our approach achieves state-of-the-art results in terms ofclassification accuracy over all learned classes.