In this paper, we analyze the secrecy capacity of a full-duplex underlay cognitive cooperative radio network (CCRN) in the presence of an eavesdropper and under the interference power constraint of a primary network. The full-duplex mode is used at the secondary relay to improve the spectrum efficiency which in turn leads to an improvement of the secrecy capacity of the full-duplex CCRN. We utilize an approximation-and-fitting method to convert the complicated expression of the signal-to-interference-plus-noise ratio into polynomial form which is then utilized to derive an expression for the secrecy capacity. Numerical results are provided to illustrate the effect of network parameters such as transmit power, interference power limit, self-interference parameters of the full-duplex mode, and distances among links on the secrecy capacity. To reveal the benefits of the full-duplex CCRN, we compare the secrecy capacity obtained when the secondary relay operates in full-duplex and half-duplex mode.