Estimating driver fatigue is an important issue for traffic safety and user-centered brain-computer interface. In this paper, based on differential entropy (DE) extracted from electroencephalography (EEG) signals, we develop a novel deep convolutional neural network to detect driver drowsiness. By exploiting DE of EEG samples, the proposed network effectively extracts class-discriminative deep and hierarchical features. Then, a densely-connected layer is used for the final decision making to identify driver condition. To demonstrate the validity of our proposed method, we conduct classification and regression experiments using publicly available SEED-VIG dataset. Further, we also compare the proposed network to other competitive state-of-the-art methods with an appropriate statistical analysis. Furthermore, we inspect the real-world usability of our method by visualizing a change in the probability of driver status and confusion matrices.