Aim: In this paper, we study a wireless-powered Internet of Things (IoT) network, where a hybrid access point (HAP) charges IoT devices with wireless energy transfer technology (WET) and collects their data by wireless information transfer (WIT). Methods: To improve spectral efficiency, we propose a hybrid non-orthogonal multiple access (NOMA)-based transmission scheme. On the one hand, NOMA technology is applied for WIT. On the other hand, when some devices transmit data, the HAP can simultaneously charge the other devices, namely concurrent WET and WIT, such that the other devices can harvest more energy to achieve a better rate with some rate loss of these devices due to interference. %During the transmission of some devices, the WET is simultaneously conducted, such that other devices can harvest more energy to achieve a better rate with a rate loss of these devices due to the interference. How to divide devices into the interference and non-interference groups, namely device grouping, and how to pair devices, e.g., device pairing, becomes critical issues in terms of the achieved network throughput and fairness. Results: We first formulate the network throughput maximization problem by optimizing the pairing and grouping policies. To simplify the analysis, we then investigate two specific hybrid NOMA-based transmission schemes. In the former, all devices are firstly paired based on the max-min criterion, where the "best" device is paired with the "worst" one, and then grouped in either ascending or descending order; this is referred to as the first-pairing-then-grouping (FPTG) scheme. In the latter, devices are first grouped and then paired; this is referred to as the first-grouping-then-pairing (FGTP) scheme. By applying the order statistics theory, we theoretically analyze the achieved network throughput and derive the corresponding pairing and grouping policies. Furthermore, we study the max-min fairness of the proposed hybrid NOMA-based scheme. Conclusion: Simulation results validate the significant improvement of the proposed hybrid NOMA-based scheme in terms of network throughput and fairness.