In this article, we propose an efficient deep-neural-network-based relay selection (DNS) scheme to evaluate and improve the end-to-end throughput in wireless-powered cognitive Internet-of-Things (IoT) networks. In this system, multiple energy harvesting (EH) relays are deployed randomly to assist data transmission from a source node to multiple users under practical nonlinearity of the EH circuits. We first design an incremental relaying protocol, where a selected user will request the help from relays if the direct transmission is not favorable. In such a protocol, we develop a deep neural network framework for relay selection and throughput prediction with high accuracy, less channel feedback amount, and short execution time. Simulation results show that the proposed DNS scheme achieves higher throughput than the conventional relay selection methods, while it considerably reduces computational complexity, suggesting a real-time configuration for IoT systems under complex scenarios. Moreover, the proposed DNS scheme achieves the root-mean-square error (RMSE) of 6.6×10 ^-3 on the considered dataset, which exhibits the lowest RMSE as compared to the state-of-the-art machine learning approaches.