Sleep staging is an important part of clinical neurology. However, it is still performed manually by technical experts and is labor-intensive and time-consuming. To overcome these obstacles in the manual sleep staging process, a large number of machine learning-based classifiers with hand-engineered features have been proposed. Additionally, combinations of a deep neural network (DNN) have been recently highlighted as the state-of-the-art classifiers in view of their effectiveness for automatic sleep staging. In spite of the existence of a large number of these types of classifiers, to-this-date, no prior DNN-based approach has attempted sleep-stage classification using pediatric electroencephalographic (EEG) signals. In this paper, we propose a novel end-to-end classifier based on a multi-domain hybrid neural network (HNN-multi) approach consisting of a convolutional neural network and bidirectional long short-term memory for automatic sleep staging with pediatric scalp EEG recordings. To find effective temporal, spatial, and domain-specific conditions, we investigated noticeable changes in the classification performance corresponding to: 1) the length of input signals; 2) the number of channels; and 3) the types of input signals in the time and frequency domains. Our HNN-based classifier yielded the best performance metrics using 30-s time series in combination with an instantaneous frequency using a 19-channel, three-stage classification, with overall accuracy, F1 score, and Cohen’s Kappa, equal to 92.21%, 0.90, and 0.88, respectively. We suggest that an effective combination of temporal and spatial time-domain clues with time-varying frequency domain information plays a pivotal role in pediatric, automatic sleep staging. Sufficiently reasonable performance of our HNN-based approach coping with the highly complicated pediatric EEG signatures hopefully sheds light on the clinical feasibility of the DNN-based automatic sleep staging for pediatric neurology.