Millimeter wave (mmWave) communications and cognitive radio technologies constitute key technologies of improving the spectral efficiency of communications. Hence, we conceive a hybrid secure precoder for enhancing the physical layer security of a cognitive mmWave wiretap channel, where a secondary transmitter broadcasts confidential information signals to multiple secondary users under the interference temperature constraint of the primary user (PU). The optimization problem is formulated as jointly optimizing the analog and digital precoder for maximizing the minimum secrecy rate of all the secondary users under practical constraints. In particular, our design satisfies the constraint on the maximum interference power received by multiple PUs, as well as the secondary users’ minimum quality-of-service (Qos), and the unit-modulus constraint on the analog precoder. Due to the non-convexity of the resultant objective function and owing to the coupling between the analog and digital precoder, the optimization problem formulated is nonconvex and nonlinear, hence it is very challenging to solve directly. Hence, we first transform it into a tractable form, and develop a penalty dual decomposition (PDD) based iterative algorithm to locate its Karush-Kuhn-Tucker (KKT) solution. Finally, we generalize the proposed PDD algorithm to a secure hybrid precoder design relying on practical finite-resolution phase shifters and show that the proposed PDD algorithm can be straightforwardly adapted to handle the scenario, where each PU is equipped with multiple antennas and the CSI of multiple eavesdroppers (Eves) is imperfectly known. Our simulation results validate the efficiency of the proposed iterative algorithm.