Aptamers are short oligonucleotides (DNA/RNA) or peptide molecules that can selectively bind to their specific targets with high specificity and affinity. As a powerful new class of amino acid ligands, aptamers have high potentials in biosensing, therapeutic, and diagnostic fields. Here, we present AptaNet—a new deep neural network—to predict the aptamer–protein interaction pairs by integrating features derived from both aptamers and the target proteins. Aptamers were encoded by using two different strategies, including k-mer and reverse complement k-mer frequency. Amino acid composition (AAC) and pseudo amino acid composition (PseAAC) were applied to represent target information using 24 physicochemical and conformational properties of the proteins. To handle the imbalance problem in the data, we applied a neighborhood cleaning algorithm. The predictor was constructed based on a deep neural network, and optimal features were selected using the random forest algorithm. As a result, 99.79% accuracy was achieved for the training dataset, and 91.38% accuracy was obtained for the testing dataset. AptaNet achieved high performance on our constructed aptamer-protein benchmark dataset. The results indicate that AptaNet can help identify novel aptamer–protein interacting pairs and build more-efficient insights into the relationship between aptamers and proteins. Our benchmark dataset and the source codes for AptaNet are available in: https://github.com/nedaemami/AptaNet.