In this paper, we study the secrecy throughput of a full-duplex wireless powered communication network (WPCN) for internet of things (IoT). The WPCN consists of a full-duplex multi-antenna base station (BS) and a number of sensor nodes. The BS transmits energy all the time, and each node harvests energy prior to its transmission time slot. The nodes sequentially transmit their confidential information to the BS, and the other nodes are considered as potential eavesdroppers. We first formulate the sum secrecy throughput optimization problem of all the nodes. The optimization variables are the duration of the time slots and the BS beamforming vectors in different time slots. The problem is shown to be non-convex. To tackle the problem, we propose a suboptimal two stage approach, referred to as sum secrecy throughput maximization (SSTM). In the first stage, the BS focuses its beamforming to blind the potential eavesdroppers (other nodes) during information transmission time slots. Then, the optimal beamforming vector in the initial non-information transmission time slot and the optimal time slots are derived. We then consider fairness among the nodes and propose max-min fair (MMF) and proportional fair (PLF) algorithms. The MMF algorithm maximizes the minimum secrecy throughput of the nodes, while the PLF tries to achieve a good trade-off between the sum secrecy throughput and fairness among the nodes. Through numerical simulations, we first demonstrate the superior performance of the SSTM to uniform time slotting and beamforming in different settings. Then, we show the effectiveness of the proposed fair algorithms.