Catastrophic forgetting is a key challenge for class-incremental learning with deep neural networks, where the performance decreases considerably while dealing with long sequences of new classes. To tackle this issue, in this paper, we propose a new exemplar-supported representation for incremental learning (ESRIL) approach that consists of three components. First, we use memory aware synapses (MAS) pre-trained on the ImageNet to retain the ability of robust representation learning and classification for old classes from the perspective of the model. Second, exemplar-based subspace clustering (ESC) is utilized to construct the exemplar set, which can keep the performance from various views of the data. Third, the nearest class multiple centroids (NCMC) is used as the classifier to save the training cost of the fully connected layer of MAS when the criterion is met. Intensive experiments and analyses are presented to show the influence of various backbone structures and the effectiveness of different components in our model. Experiments on several general-purpose and fine-grained image recognition datasets have fully demonstrated the efficacy of the proposed methodology. INDEX TERMS Exemplar-based subspace clustering, incremental learning, memory aware synapses, image recognition.