While the deep convolutional neural networks (DCNNs) have shown excellent performance in various applications, such as image classification, training a DCNN model from scratch is computationally expensive and time consuming. In recent years, a lot of studies have been done to accelerate the training of DCNNs, but most of them were performed in a one-time manner. Considering the learning patterns of the human beings, people typically feel more comfortable to learn things in an incremental way and may be overwhelmed when absorbing a large amount of new information at once. Therefore, we demonstrate a new training schema that splits the whole training process into several sub-training steps. In this study, we propose an efficient DCNN training framework where we learn the new classes of concepts incrementally. The experiments are conducted on CIFAR-100 with VGG-19 as the backbone network. Our proposed framework demonstrates a comparable accuracy compared with the model trained from scratch and has shown 1.42x faster training speed.