Mobile edge computing (MEC) integrated with wireless power transfer (WPT) has became a promising trend to shorten task delay and prolong battery life of wireless devices (WDs). Introducing the relay technique to WPT-MEC system can improve offloading capability and energy efficiency, particularly in the scenarios of poor wireless channel conditions between the server and WDs. In this paper, we focus on maximizing the energy efficiency (EE) of a multi-user relay-aided WPT-MEC system. The joint optimization of the configuration of relay, wireless charge time fraction, and decision of WDs’ offloading strategy presents significant challenges due to the combination of multi-user computing mode selection and strong coupling of transmission time allocation for each WD. To address these challenges, we formulate the problem as a mixed integer nonlinear programming (MINLP) problem and propose an efficient iterative algorithm called MSRA to solve it. Our approach leverages Dinkelbach’s method to transform the original problem into a tractable problem. Furthermore, we employ the alternating direction method of multipliers (ADMM) technique to decompose the problem into multiple subproblems, thereby avoiding the combination of computing mode selection at each WD and hence enabling parallel computation. Within each iteration step of the ADMM-based algorithm, we develop a DAI-Based algorithm to handle the strong coupling with offloading time allocation that incorporates a Bisection Search algorithm with constant time complexity and solves a standard convex problem. Extensive simulation results demonstrate the effectiveness of our proposed algorithm as evidenced by its rapid convergence and impressive energy efficiency imporvement of over 15% compared to benchmark methods.