In this paper, we investigate resource allocation algorithm design for full-duplex (FD) cognitive radio systems. The secondary network employs a FD base station for serving multiple half-duplex downlink and uplink users simultaneously. We study the resource allocation design for minimizing the maximum interference leakage to primary users while providing quality of service for secondary users. The imperfectness of the channel state information of the primary users is taken into account for robust resource allocation algorithm design. The algorithm design is formulated as a non-convex optimization problem and solved optimally by applying semidefinite programming (SDP) relaxation. Simulation results not only show the significant reduction in interference leakage compared to baseline schemes, but also confirm the robustness of the proposed algorithm.