In this work, we investigate a joint transmit beamforming and artificial noise (AN) covariance matrix design in a multiple-input multiple-output (MIMO) cognitive radio (CR) downlink network with simultaneous wireless information and power transfer (SWIPT), where the malicious energy receivers (ERs) may decode the desired information and hence can be treated as potential eavesdroppers (Eves). In order to improve the secure performance of the transmission, AN is embedded to the information-bearing signal, which acts as interference to the Eves and provides energy to all receivers. Specifically, this joint design is studied under a practical non-linear energy harvesting (EH) model, our aim is to maximize the secrecy rate at the SR subject to the transmit power budget, EH constraints and quality of service (QoS) requirement. The original problem is not convex and challenging to be solved. To circumvent its intractability, an equivalent reformulation of this secrecy rate maximization (SRM) problem is introduced, wherein the resulting problem is primal decomposable and thus can be handled by alternately solving two convex subproblems. Finally, numerical results are presented to verify the effectiveness of our proposed scheme.