Unmanned aerial vehicles (UAVs) have been actively studied as moving cloudlets to provide application offloading opportunities and to enhance the security level of user equipments (UEs). In this correspondence, we propose a hybrid UAV-aided secure offloading system in which a UAV serves as a helper by switching the mode between jamming and relaying to maximize the secrecy sum-rate of UEs. This work aims to optimize (i) the trajectory of the helper UAV, (ii) the mode selection strategy and (iii) the UEs' offloading decisions under the constraints of offloading accomplishment and the UAV's operational limitations. The solution is provided via a deep deterministic policy gradient (DDPG)-based method, whose superior performance is verified via a numerical simulation and compared to those of traditional approaches.