Unmanned Aerial Vehicles (UAV)-enabled communication is a promising solution for secure air-to-ground (A2G) networks due to the additional secure degrees of freedom afforded by mobility. However, the jittering characteristics caused by the random airflow and the body vibration of the UAV itself have a non-negligible impact on the performance of UAV communication. Considering the impact of UAV jittering, this paper propose a robust and secure transmission design assisted by an novel active intelligent reflecting surface (IRS),where the reflecting elements in IRS not only adjust the phase shift but also amplify the amplitude of signals. Specifically, under the worst-case secrecy rate constraints, we aim to minimize the transmission power by the robust joint design of active IRS's reflecting coefficient and beamforming at the UAV-borne base station (UBS). However,it is challenging to solve the joint optimization problem due to its non-convexity. To tackle this problem, the non-convex problem is reformulated with linear approximation for the channel variations and linear matrix inequality transformed by S-procedure and Schur's complement. Then, we decouple this problem into two sub-problems, namely, passive beamforming and active IRS's reflecting coefficient optimization, and solve them through alternate optimization (AO). Finally, the numerical results demonstrate the potential of active IRS on power saving under secure transmission constraints and the impact of UAV jittering.