In this paper, we propose a secure unmanned aerial vehicle (UAV) mobile edge computing (MEC) system where multiple ground users offload large computing tasks to a nearby legitimate UAV in the presence of multiple eavesdropping UAVs with imperfect locations. To enhance security, jamming signals are transmitted from both the full-duplex legitimate UAV and non-offloading ground users. For this system, we design a low-complexity iterative algorithm to maximize the minimum secrecy capacity subject to latency, minimum offloading and total power constraints. Specifically, we jointly optimize the UAV location, users’ transmit power, UAV jamming power, offloading ratio, UAV computing capacity, and offloading user association. Numerical results show that our proposed algorithm significantly outperforms baseline strategies over a wide range of UAV selfinterference (SI) efficiencies, locations and packet sizes of ground users. Furthermore, we show that there exists a fundamental tradeoff between the security and latency of UAV-enabled MEC systems which depends on the UAV SI efficiency and total UAV power constraints.