This paper studies optimal resource allocation in the wireless-powered communication network (WPCN), where one hybrid access-point (H-AP) operating in full-duplex (FD) broadcasts wireless energy to a set of distributed users in the downlink (DL) and at the same time receives independent information from the users via time-division-multiple-access (TDMA) in the uplink (UL). We design an efficient protocol to support simultaneous wireless energy transfer (WET) in the DL and wireless information transmission (WIT) in the UL for the proposed FD-WPCN. We jointly optimize the time allocations to the H-AP for DL WET and different users for UL WIT as well as the transmit power allocations over time at the H-AP to maximize the users' weighted sum-rate of UL information transmission with harvested energy. We consider both the cases with perfect and imperfect self-interference cancellation (SIC) at the H-AP, for which we obtain optimal and suboptimal time and power allocation solutions, respectively. Furthermore, we consider the half-duplex (HD) WPCN as a baseline scheme and derive its optimal resource allocation solution. Simulation results show that the FD-WPCN outperforms HD-WPCN when effective SIC can be implemented and more stringent peak power constraint is applied at the H-AP.