Deep learning-based methods have reached state of the art performances, relying on a large quantity of available data and computational power. Such methods still remain highly inappropriate when facing a major open machine learning problem, which consists of learning incrementally new classes and examples over time. Combining the outstanding performances of Deep Neural Networks (DNNs) with the flexibility of incremental learning techniques is a promising venue of research. In this contribution, we introduce Transfer Incremental Learning using Data Augmentation (TILDA). TILDA is based on pre-trained DNNs as feature extractors, robust selection of feature vectors in subspaces using a nearest-class-mean based technique, majority votes and data augmentation at both the training and the prediction stages. Experiments on challenging vision datasets demonstrate the ability of the proposed method for low complexity incremental learning, while achieving significantly better accuracy than existing incremental counterparts.