We propose a cooperative cognitive radio network (CCRN) with secondary users (SUs) employing two simultaneous transmit and receive (STAR) antennas. In the proposed framework of full-duplex (FD) multiple-input-multiple-output (MIMO) CCRN, the region of achievable rate is expanded via FD communication among SUs enabled by the STAR antennas adopted for the SUs. The link capacity of the proposed framework is analyzed theoretically. It is shown through numerical analysis that the proposed FD MIMO-CCRN framework can provide a considerable performance gain over the conventional frameworks of CCRN and MIMO-CCRN.