Antiviral peptides (AVPs) are a group of biological peptide molecules which can inhibit virus infection. In recent years, AVPs, as a new viral therapy, have attracted more and more attention. Therefore, how to quickly and accurately identify new AVPs is particularly important. In the past few years, researchers have proposed a variety of traditional machine learning methods based on feature engineering to predict AVPs. But how to select effective features requires much domain knowledge. To solve this problem, we proposed a hybrid neural network combining the advantages of convolutional neural network and long short-term memory (LSTM) for the prediction of AVPs. To be specific, we use the convolution layer to learn local patterns, and then use LSTM to describe the order in which these patterns may appear in AVPS. In addition, attention mechanism was introduced into the model to selectively enhance features. Through a variety of experimental tests, the results show that the model has achieved excellent performance. It can be used as one of the effective tools to predict AVPs.