Automatic sleep stage scoring is of great importance for investigating sleep architecture during infancy. In this work, we introduce a novel multichannel approach based on deep learning networks and hidden Markov models (HMM) to improve the accuracy of sleep stage classification in term neonates. The classification performance was evaluated on quiet sleep (QS) and active sleep (AS) stages, each with two substates, using multichannel EEG data recorded from sixteen neonates with postmenstrual age of 38–40 weeks. A comprehensive set of linear and nonlinear features were extracted from thirty-second EEG segments. The feature space dimensionality was then reduced by using an evolutionary feature selection method called MGCACO (Modified Graph Clustering Ant Colony Optimization) based on the relevance and redundancy analysis. A bi-directional long-short time memory (BiLSTM) network was trained for sleep stage classification. The number of channels was optimized using the sequential forward selection (SFS) method to reduce the spatial space. Finally, an HMM-based postprocessing stage was used to reduce false positive by incorporating the knowledge of transition probabilities between stages into the classification process. The method performance was evaluated using the K-fold (KFCV) and leave-one-out cross validation (LOOCV) strategies. Using six-bipolar channels, our method achieved a mean kappa and an overall accuracy of 0.71 (0.76) and 78.9% (82.4%) using the KFCV and LOOCV strategies, respectively. The presented automatic sleep stage scoring method can be used to study the neurodevelopmental process and to diagnose brain abnormalities in term neonates.