This paper studies intelligent reflecting surface (IRS)-aided full-duplex (FD) wireless-powered communication network (WPCN), where a hybrid access point (HAP) broadcasts energy signals to multiple devices for their energy harvesting in the downlink (DL) and meanwhile receives information signals in the uplink (UL) with the help of IRS. We propose a fully dynamic IRS beamforming design, where the IRS phase-shift vectors vary with each time slot for both DL wireless energy transfer (WET) and UL wireless information transmission (WIT). We aim to maximize the system throughput by jointly optimizing the time allocation, HAP transmit power, and IRS phase shifts. Since the formulated problem is non-convex due to the highly coupled optimization variables in the objective function and non-convex unit-modulus constraints of phase shifts, we propose a novel penalty-based algorithm consisting of a two-layer iteration, i.e., an inner layer iteration and an outer layer iteration. Specifically, the inner layer solves the penalized optimization problem, while the outer layer updates the penalty coefficient over iterations to guarantee convergence. Simulation results demonstrate that integrating IRS into WPCN significantly improve the system throughput and also unveil that the IRS-aided FD-WPCN is particularly beneficial for the large number of devices scenario.