With the continuous development of B5G/6G cellular networks, the explosive growth of mobile Internet services and the resulting tremendous traffic demand have led to a significantly heavy pressure on how to efficiently satisfy the users’ traffic demands with guaranteed quality of services, especially the coverage at the cell-edge. Thanks to the advantage in flexible deployment, the unmanned aerial vehicle (UAV) has been considered as a promising approach for providing efficient data access for cell-edge users (CEUs), which usually suffer from a poor connection to the cellular base stations (BSs). In this paper, we consider a scenario of a group of CEUs with each CEU having both the task of delivering data to the cellular BS (i.e., the data-transmission task) and the task of completing a given computation workload (i.e., the computation-task). Meanwhile, we consider that the UAV serves as a dual-role (DUAV), i.e., the relay for forwarding CEUs’ data to the cellular BS, and the edge-server for processing the CEUs’ offloaded computation workloads. Taking into account that a malicious node which overhears the DUAV’s relay transmission, we investigate the secrecy driven UAV assisted relay transmission via cooperative computation offloading, in which we exploit the CEUs’ computation-offloading transmission to provide cooperative jamming to the malicious node who overhears the DUAV’s relay transmission. Specifically, we formulate a joint optimization of the DUAV’s hovering position, transmit-power and computation-rate allocation as well as the CEUs’ transmission duration and computation offloading, with the objective of minimizing the total energy consumption of the DUAV and all CEUs. Despite the non-convexity of the formulated joint optimization problem, we propose an efficient algorithm for finding the optimal solution. With the optimal offloading and transmission solutions provided by the polyblock approximation based algorithm (PA-Algorithm) under the given hovering point as a subroutine, we further optimize the DUAV’s hovering position by proposing a precoding-based Cross-Entropy algorithm (PBCE-Algorithm) for finding the DUAV’s optimal hovering position. In particular, by properly precoding the feasible region for hovering, our PBCE-Algorithm can outperform some existing algorithms in terms of accuracy and efficiency. To further reduce the computational complexity, we also propose a low-complexity algorithm for solving the joint optimization problem. Numerical results demonstrate the efficiency of our proposed algorithms and the performance advantage of our proposed secrecy driven UAV assisted relay transmission via cooperative computation offloading.