For EEG-based drowsiness recognition, it is desirable to use subject-independent recognition since conducting calibration on each subject is time-consuming. In this paper, we propose a novel Convolutional Neural Network (CNN)-Long Short-Term Memory (LSTM) model for subject-independent drowsiness recognition from single-channel EEG signals. Different from existing deep learning models that are mostly treated as black-box classifiers, the proposed model can explain its decisions for each input sample by revealing which parts of the sample contain important features identified by the model for classification. This is achieved by a visualization technique by taking advantage of the hidden states output by the LSTM layer. Results show that the model achieves an average accuracy of 72.97% on 11 subjects for leave-one-out subject-independent drowsiness recognition on a public dataset, which is higher than the conventional baseline methods of 55.42%-69.27%, and state-of-the-art deep learning methods. Visualization results show that the model has discovered meaningful patterns of EEG signals related to different mental states across different subjects.