Abstract: Unmanned aerial vehicle (UAV) terahertz communication has the advantages of both extremely high bandwidth and flexible deployment, which provides a good solution to meet the demanding communication requirements of 6G. However, the UAV platform's susceptibility to environmental influences such as wind and the time-varying nature of its communication links make it difficult to obtain perfect channel state information (CSI) , thus hindering the establishment of robust and stable secure communication links with ground users. In this research, an artificial noise-assisted robust optimization algorithm is proposed for secure downlink terahertz UAV communication with imperfect CSI. Specifically, with imperfect CSI at both users and eavesdroppers, artificial noise was introduced to enhance the secure communication. The objective was to minimize the total transmission power of the UAV by optimizing the beamforming vectors, artificial noise vectors, and UAV trajectory, under the constraints of worst-case user communication performance and worst-case eavesdropping rate. The problem, characterized as a non-convex polynomial with parameter uncertainties, was addressed by developing an alternating iterative algorithm based on semidefinite relaxation, S-procedure, and successive convex approximation. Equivalent transformations were used to convert the original fractional constraints with parameter uncertainties into linear matrix inequality constraints. Simulation results show that compared with benchmark algorithms, the proposed algorithm effectively reduces the total transmission power of the base station and achieves robust, energy-efficient secure communication under imperfect CSI conditions.