This article investigates intelligent reflecting surface (IRS)-assisted wireless-powered Internet of Things (IoT) networks. Specifically, multiple IoT devices first collect energy radiated from a power station (PS), then each device uses its harvested energy to support data transmission to an access point (AP) via frequency-division multiple access (FDMA). In addition, an IRS aims to improve wireless energy transfer (WET) and wireless information transfer (WIT) capabilities using passive reflection beamformers. The system sum throughput, as a performance metric, is maximized evaluate the overall performance of the considered model, which is subject to the constraints of IRS phase shifts, transmission time scheduling, and bandwidth allocation. This problem is not convex with respect to multiple coupled variables, and cannot be directly solved. To circumvent this nonconvexity, the transmission time scheduling and the bandwidth allocation are optimally designed in the closed form by the Lagrange dual method and the Karush–Kuhn–Tucker (KKT) conditions. Moreover, an alternating optimization (AO) algorithm is used to optimally design the IRS’s phase shifts during the WET and WIT phases in an alternating fashion. Specifically, we propose elementwise block coordinate decent (EBCD) and complex circle manifold (CCM) algorithms to iteratively derive the optimal phase shifts in the closed form. We also characterize the convergence behavior of the proposed algorithms. Finally, numerical results are presented to validate the performance of the proposed scheme, where the benefits of the IRS are highlighted in terms of sum throughput, transmission time scheduling, and energy harvesting, compared with the benchmark schemes.