In this article, with the aim to enhance the secure transmission and improve the utilization of spectrum resources in Internet of Things (IoT), a multicarrier nonorthogonal multiple access (MC-NOMA)-assisted full duplex (FD) network is investigated, in which nonorthogonal multiple access (NOMA) is implemented in both uplink and downlink transmissions. The lightweight and low-power physical layer security (PLS) technology is employed to protect the information from eavesdropping. Taking the imperfect channel state information (CSI) into account, we formulate a problem to optimize the beamforming vector, artificial noise (AN), transmit power, and subcarrier assignment policy aiming to maximize the worst case sum secrecy rate under the Quality of Service (QoS) and power consumption constraints. Since the formulated problem is nonconvex and difficult to be solved, we decompose it into two joint optimization subproblems. The first is resource allocation with given subcarrier assignment, which is solved by using the block coordinate descent (BCD) approach. The second is subcarrier assignment solved by the matching theory. Our simulation shows that the proposed scheme is robust against the CSI imperfectness of the eavesdropping and self-interference channels, while providing significant sum secrecy rate improvement compared with the orthogonal multiple access (OMA), half duplex (HD) systems, and other benchmark schemes.