Unmanned aerial vehicle (UAV) is a promising communication platform to assist terrestrial networks. In this work, we aim to provide relay communication to the blocked or low-quality terrestrial networks via an aerial relay. Nevertheless, major issues of the considered system are the worrying security and limited service time. Thus, we study a novel aerial relay system via collaborative beamforming (CB) by exploiting a UAV-enabled virtual antenna array (UVAA) to achieve a secure and energy-efficient communication for remote ground users (GUs). Specifically, we formulate a secure and energy-efficient communication multi-objective optimization problem (SECMOP) to circumvent the effects of the known and unknown eavesdroppers and minimize the propulsion energy consumption of UAVs, by optimizing the hovering positions and excitation current weights of UAVs and the scheduling for communicating with the remote GUs. The formulated SECMOP is challenging and proven to be NP-hard. Thus, we propose an improved evolutionary computation method with several enhanced designs to solve this problem. Simulation results demonstrate the benefits of the proposed IMODAOM against various benchmark algorithms. Moreover, we find that the UVAA-based relay can achieve substantial energy consumption reduction as compared to the multi-hop relay scheme.