As the continuous emergence of new applications, such as face recognition and automatic driving, wireless devices are faced with problems, for instance, limited computing resources and excessive energy consumption. Thus, this study presents a joint task offloading and computation algorithm for multi-carrier and multi-relay mobile edge computing (MEC) systems to resolve aforementioned problems. First, we build a multi-carrier and multi-relay MEC system. Next, we calculate the delay constraints according to the given tasks, optimize resource allocation. To optimize the total energy consumed of relays and users, the optimization of resource allocation is expressed as a mixed integer programming problem. Further, because difficulty in solving the issue, we use continuous relaxation and algebraic transformation to convert the problem to equivalent problem. Finally, we solve the problem utilizing the interior point method, which realizing the highly efficient resource allocation. Simulation results demonstrated that the presented joint collaborative task offloading and computing program decreases energy consumed by 26.67% compared with the relay-only assisted task computing program.