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The combination of unmanned aerial vehicles (UAVs) and mobile edge computing (MEC) is considered as a promising approach to tackle soaring computing requirements. The broadcast nature of air‐to‐ground (A2G) links makes UAV communications vulnerable to eavesdroppers, so secure UAV communications remain an open question. This paper proposes a secure communication scheme for reconfigurable intelligent surface (RIS)‐assisted UAV‐MEC systems, in which the RIS assists the user in offloading data to the legitimate UAV, and the legitimate UAV provides computing services to the user. To fully expand the security computing capacity of the system, the communication link is improved by introducing RIS, and the jammer interferes with the eavesdropper. The secure computing capability of the system is maximized by optimizing communication resources and trajectories. Since the proposed problem is non‐convex, successive convex approximation (SCA) technique and block coordinate descent (BCD) technique is combined to solve the problem. The simulation results show that the proposed scheme in this paper can effectively improve the system secure computing bits compared with the benchmark scheme. [ABSTRACT FROM AUTHOR]