In this paper, we investigate beamforming design for cooperative secure transmission in cognitive two-way relay networks, where the cognitive transmitter (CT) with multiple antennas helps to forward the signals of two primary transmitters (PTs) and tries to protect the PTs from wiretapping by a single-antenna eavesdropper. With the objective of maximizing the secrecy sum rate (SSR) for PTs, we jointly design the beamforming matrix for the PTs' signals, the beamforming vector for the cognitive receiver (CR)'s signal, and the artificial noise (AN)'s beamforming matrix, under the quality of service constraint at the CR and the transmit power constraint at the CT. We propose the monotonic optimization-based algorithm to obtain the global optimal solution to the SSR maximization problem, which is a double-layer iterative algorithm and has very high complexity. To balance the complexity and the performance, we also propose a sequential parametric convex approximation-based single-layer iterative algorithm and a zero-forcing-based closed-form algorithm, the latter of which has the lowest complexity. Furthermore, we derive the asymptotic achievable secrecy sum rate when the CT transmit power goes to infinity. We present the numerical results to verify the effectiveness of our proposed algorithms.