Viruses pose a great threat to human production and life, thus the research and development of antiviral drugs is urgently needed. Antiviral peptides play an important role in drug design and development. Compared with the time-consuming and laborious wet chemical experiment methods, it is critical to use computational methods to predict antiviral peptides accurately and rapidly. However, due to limited data, accurate prediction of antiviral peptides is still challenging and extracting effective feature representations from sequences is crucial for creating accurate models. This study introduces a novel two-step approach, named HybAVPnet, to predict antiviral peptides with a hybrid network architecture based on neural networks and traditional machine learning methods. We adopted a stacking-like structure to capture both the long-term dependencies and local evolution information to achieve a comprehensive and diverse prediction using the predicted labels and probabilities. Using an ensemble technique with the different kinds of features can reduce the variance without increasing the bias. The experimental result shows HybAVPnet can achieve better and more robust performance compared with the state-of-the-art methods, which makes it useful for the research and development of antiviral drugs. Meanwhile, it can also be extended to other peptide recognition problems because of its generalization ability.