We consider physical-layer security in a novel MISO cooperative overlay cognitive radio network (CRN) with a single eavesdropper. We aim to design an artificial noise (AN) aided secondary transmit strategy to maximize the joint achievable secrecy rate of both primary and secondary links, subject to a global secondary transmit power constraint and guaranteeing any transmission of secondary should at least not degrade the receive quality of primary network, under the assumption that global CSI is available. The resulting optimization problem is challenging to solve due to its non-convexity in general. A computationally efficient approximation methodology is proposed based on the semidefinite relaxation (SDR) technique and followed by a two-step alternating optimization algorithm for obtaining a local optimum for the corresponding SDR problem. This optimization algorithm consists of a one-dimensional line search and a non-convex optimization problem, which, however, through a novel reformulation, can be approximated as a convex semidefinite program (SDP). Analysis on the extension to multiple eavesdroppers scenario is also provided. Simulation results show that the proposed AN-aided joint secrecy rate maximization design (JSRMD) can significantly boost the secrecy performance over JSRMD without AN.