This work focuses on the optimal trajectory of a rotary‐wing unmanned aerial vehicle (UAV) jammer and the system power allocation with the objective of maximizing the total secure energy efficiency (EE) of a slotted relay‐assisted millimeter wave (mm‐Wave) cognitive radio system. The UAV flies from starting location to final one in a round of communication mission that is overheard by a malicious eavesdropper. The network terminals are equipped with multiple‐input multiple‐output (MIMO) antenna array. This work first develops a practical approximation propagation model by addressing three key challenges: path loss, small‐scale Nakagami‐m fading channel gains, and transceiver antenna beamforming gains. By using the approximate model, the upper and lower bounds of the ergodic rate of each communication link are derived. Second, with the objective of maximizing secure EE, the optimal UAV trajectory and system resource allocation framework is established by considering the constraints of interference at primary receiver (PR), information‐causality relationship, rotary‐wing UAV propulsion energy and so forth. The optimal framework is solved with a tractable CVX tool by using the derived upper and lower bounds and successive convex approximation. Finally, an iterative optimizing algorithm is established by using Dinkelbach's method. In the simulation, the work presents the comparison of UAV trajectories, secure rates, and secure EEs of three schemes, that is, the proposed EE scheme, the non‐EE scheme where only the optimal secure rate is considered, and the EE scheme with the consideration of all communication‐related energy consumption. The simulations show that the EE schemes achieve smoother UAV trajectory than non‐EE, but the non‐EE scheme has higher secure rate. The impact of communication energy consumption is negligible. In addition, the effect of MIMO antenna array and mm‐Wave on system performance is exploited.