We propose a joint optimization of beamforming and time allocation for full-duplex (FD) wireless-powered communication networks (WPCNs). In FD-WPCNs, an FD-enabled hybrid access point (HAP) having multiple antennas broadcasts radio frequency (RF) energy to users, and concurrently each user transmits its own information to the HAP. Due to a lack of fixed power supplies at the users, it is difficult for the HAP to have accurate channel state information (CSI) of all links. Therefore, in this letter, a robust algorithm is proposed to maximize the weighted sum rate of the users against the uncertainty of the CSI using the relationship between the weighted sum rate and the weighted sum of mean-square error. Numerical results demonstrate that the proposed algorithm provides robustness against imperfect channel knowledge and benefits of utilizing multiple antennas in the FD-WPCNs.