Cancer is a well-known killer of human beings, which has led to countless deaths and misery. Anticancer peptides open a promising perspective for cancer treatment, and they have various attractive advantages. Conventional wet experiments are expensive and inefficient for finding and identifying novel anticancer peptides. There is an urgent need to develop a novel computational method to predict novel anticancer peptides. In this study, we propose a deep learning long short-term memory (LSTM) neural network model, ACP-DL, to effectively predict novel anticancer peptides. More specifically, to fully exploit peptide sequence information, we developed an efficient feature representation approach by integrating binary profile feature and k-mer sparse matrix of the reduced amino acid alphabet. Then we implemented a deep LSTM model to automatically learn how to identify anticancer peptides and non-anticancer peptides. To our knowledge, this is the first time that the deep LSTM model has been applied to predict anticancer peptides. It was demonstrated by cross-validation experiments that the proposed ACP-DL remarkably outperformed other comparison methods with high accuracy and satisfied specificity on benchmark datasets. In addition, we also contributed two new anticancer peptides benchmark datasets, ACP740 and ACP240, in this work.