This paper makes an investigation of a secure unmanned aerial vehicle (UAV)-aided communication network based on directional modulation (DM). In this network, ground base station (GBS) acts as a control center to transmit confidential message and artificial noise (AN). The UAV user, moving along a linear flight trajectory, is intended to receive the useful information from GBS. At the same time, it also sends AN signals to further interference eavesdropper’s channel. Aiming at maximizing secrecy rate during the UAV flight process, a joint optimization problem is formulated with respect to power allocation (PA) factors, beamforming vector and AN projection matrices. For simplicity, maximum rate transmission, nullspace projection and the leakage-based method are applied to form the transmit beamforming vector, AN projection matrix at GBS, and AN projection vector at UAV user, respectively. Following this, the optimization problem reduces to a bivariate optimization programme with two PA factors. An alternating iterative algorithm (AIA) is proposed to optimize the two PA factors. Simulation results demonstrate that, compared to the half-duplex (HD) mode, the proposed strategy for full-duplex (FD) mode achieves a higher secrecy rate (SR) and outperforms the FD mode with fixed PA strategy.